Samacheer Kalvi Class 10 Science Solutions Chapter 1 Laws of Motion

I. Choose The Correct Answer

Question 1. Inertia of a body depends on:
(a) weight of the object
(b) acceleration due to gravity of the planet
(c) mass of the object
(d) both (a) & (b)
Answer: (c) mass of the object
In simple words: How much a body resists changes to its motion depends on its mass. The more mass it has, the harder it is to move or stop.

🎯 Exam Tip: Remember that inertia is a direct measure of mass. A heavier object has more inertia, meaning it's harder to start or stop moving.

Question 2. Impulse is equals to _____.
(a) rate of change of momentum
(b) rate of force and time
(c) change of momentum
(d) rate of change of mass.
Answer: (c) change of momentum
In simple words: Impulse is the total change in an object's momentum. It is like the "push" or "hit" an object receives, which changes how fast and in what direction it is moving.

🎯 Exam Tip: Impulse is literally defined as the change in momentum. The unit of impulse (Newton-second) is the same as the unit of momentum (kg m/s).

Question 3. Newton's III law is applicable:
(a) for a body is at rest
(b) for a body in motion
(c) both (a) & (b)
(d) only for bodies with equal masses
Answer: (c) both (a) & (b)
In simple words: Newton's third law, which states that for every action there is an equal and opposite reaction, applies to objects whether they are sitting still or moving. It is a fundamental law of interaction between objects.

🎯 Exam Tip: Newton's third law describes interactions between objects and applies universally, regardless of their state of motion or mass. Focus on the 'interaction' aspect for full marks.

Question 4. Plotting a graph for momentum on the X-axis and time on Y-axis. Slope of momentum – time graph gives _____.
(b) Acceleration
(c) Force
(d) Rate of force.
Answer: (c) Force
In simple words: If you draw a graph where momentum is on the X-axis and time is on the Y-axis, the slope of that line will show you the force. This is because force is how quickly momentum changes over time.

🎯 Exam Tip: Recall Newton's second law: \( F = \frac{\Delta p}{\Delta t} \). This directly relates force to the rate of change of momentum, which is represented by the slope on a momentum-time graph.

Question 5. In which of the following sport the turning effect of force is used?
(a) swimming
(b) tennis
(c) cycling
(d) hockey
Answer: (c) cycling
In simple words: When you ride a bicycle, you use your hands to turn the handlebars. This turning action is an example of applying a force to create a turning effect, which is called torque, to steer the bike.

🎯 Exam Tip: The "turning effect of force" is also known as torque or moment of force. It's essential for sports and activities involving rotation, like steering or pedaling.

Question 6. The unit of 'g' is \( \text{ms}^{-2} \). It can be also expressed as:
(a) \( \text{cm s}^{-2} \)
(b) \( \text{N kg}^{-1} \)
(c) \( \text{N m}^{2}\text{kg}^{-1} \)
(d) \( \text{cm}^{2}\text{s}^{-2} \)
Answer: (a) \( \text{cm s}^{-2} \)
In simple words: The unit for 'g' (acceleration due to gravity) is usually meters per second squared. This can also be written as centimeters per second squared, just in a different unit system, but the meaning is the same.

🎯 Exam Tip: Acceleration is change in velocity over time, so its units are always (distance)/(time) squared. While \( \text{N kg}^{-1} \) is also a valid unit for 'g' (from \( F = mg \)), the options were looking for a direct conversion of the acceleration unit itself.

Question 7. One kilogram force equals to _____.
(a) 9.8 dyne
(b) \( 9.8 \times 10^4 \text{ N} \)
(c) \( 98 \times 10^4 \text{ dyne} \)
(d) 980 dyne.
Answer: (c) \( 98 \times 10^4 \text{ dyne} \)
In simple words: One kilogram-force is the force caused by gravity on a 1-kilogram mass. This is equal to 9.8 Newtons, which can also be written as \( 98 \times 10^4 \) dynes when converting to a smaller unit of force.

🎯 Exam Tip: Remember the conversion factor between Newton and dyne: \( 1 \text{ N} = 10^5 \text{ dyne} \). Also, \( 1 \text{ kgf} = 9.8 \text{ N} \). Combine these to get the answer.

Question 8. The mass of a body is measured on planet Earth as M kg. When it is taken to a planet of radius half that of the Earth then its value will be ..... kg.
(a) 4 M
(b) 2 M
(c) M/4
(d) M
Answer: (d) M
In simple words: Mass is how much "stuff" an object is made of. It does not change based on where the object is located. So, if an object has mass M on Earth, it will still have mass M on another planet, no matter its size.

🎯 Exam Tip: Distinguish between mass and weight. Mass is an intrinsic property of an object and remains constant, while weight is the force of gravity acting on an object and changes with gravitational acceleration.

Question 9. If the Earth shrinks to 50% of its real radius its mass remaining the same, the weight of a body on the Earth will:
(a) decrease by 50%
(b) increase by 50%
(c) decrease by 25%
(d) increase by 300%
Answer: (d) increase by 300%
In simple words: If the Earth gets smaller but keeps the same amount of mass, gravity on its surface would get much stronger. This means an object's weight would increase a lot because gravity would be pulling it with more force.

🎯 Exam Tip: Recall the formula for gravitational acceleration \( g = \frac{GM}{R^2} \). If R is halved (50%), then \( R^2 \) becomes \( (R/2)^2 = R^2/4 \). So \( g \) would become \( \frac{GM}{R^2/4} = 4 \frac{GM}{R^2} = 4g \). Weight \( W = mg \), so new weight \( W' = m(4g) = 4W \). This is an increase of 300% (4 times the original value means an increase of 3 times the original value, or 300%).

Question 10. To project the rockets which of the following principle(s) is / (are) required?
(a) Newton's third law of motion
(b) Newton's law of gravitation
(c) law of conservation of linear momentum
(d) both a and c.
Answer: (d) both a and c.
In simple words: Rockets work because of two main physics rules. First, they push hot gas out one way, and the gas pushes the rocket the other way (Newton's third law). Second, the total push, or momentum, stays the same before and after the gas is expelled (conservation of linear momentum).

🎯 Exam Tip: Rocket propulsion is a classic example of Newton's third law in action, where the action of expelling gas causes an equal and opposite reaction force on the rocket. This also directly demonstrates the conservation of linear momentum for the rocket-gas system.

II. Fill In The Blanks

Question 1. To produce a displacement ........ is required.
Answer: force
In simple words: You need a force to make something move from one place to another.

🎯 Exam Tip: Remember that force is what causes motion or changes in motion. Without force, an object at rest stays at rest, and an object in motion stays in motion.

Question 2. Passengers lean forward when the sudden brake is applied in a moving vehicle. This can be explained by ..........
Answer: inertia
In simple words: When a car stops suddenly, your body wants to keep moving forward because of inertia, making you lean ahead.

🎯 Exam Tip: Inertia is an object's resistance to any change in its state of motion. In this case, your body's inertia of motion makes it continue forward even when the car stops.

Question 3. By convention, the clockwise moments are taken as ..... and the anticlockwise moments are taken as ..........
Answer: negative, positive
In simple words: When something turns in a clockwise direction, we usually call that a negative turn. If it turns the other way, anti-clockwise, we call it a positive turn.

🎯 Exam Tip: This is a sign convention in physics. Consistently applying this convention (e.g., clockwise as negative, anti-clockwise as positive) is crucial for solving problems involving moments and torque.

Question 4. .......... is used to change the speed of the car.
Answer: Accelerator
In simple words: The accelerator pedal in a car is used to either speed up or slow down the vehicle. When you push it, the car goes faster, and when you release it, the car slows down.

🎯 Exam Tip: The accelerator controls the engine's power, which in turn changes the force applied to the wheels, altering the car's speed. It is responsible for making the car accelerate (speed up) or decelerate (slow down).

Question 5. A man of mass 100 kg has a weight of ........ at the surface of the Earth.
Answer: \( 980 \text{ N} \)
In simple words: To find a man's weight on Earth, you multiply his mass (100 kg) by the strength of Earth's gravity (9.8 m/s²). This gives a weight of 980 Newtons.

🎯 Exam Tip: Always remember the formula \( \text{Weight} = \text{mass} \times \text{acceleration due to gravity} \). On Earth, 'g' is approximately \( 9.8 \text{ m/s}^2 \), so \( \text{Weight} = 100 \text{ kg} \times 9.8 \text{ m/s}^2 = 980 \text{ N} \).

III. State Whether The Following Statements Are True Or False. Correct The Statement If It Is False.

Question 1. The linear momentum of a system of particles is always conserved.
Answer: True
In simple words: In a group of particles, the total amount of linear momentum always stays the same, as long as no outside forces act on it.

🎯 Exam Tip: This is the law of conservation of linear momentum. It holds true only in an isolated system, meaning no external forces are acting on the system.

Question 2. Apparent weight of a person is always equal to his actual weight.
Answer: False - Apparent weight of a person is not always equal to his actual weight.
In simple words: How heavy you feel (apparent weight) is not always the same as your actual weight. For example, in an elevator, you might feel lighter or heavier depending on its movement.

🎯 Exam Tip: Apparent weight can differ from actual weight in accelerating frames of reference, such as an elevator moving up or down, or in free fall. It only matches actual weight when the person is at rest or moving at a constant velocity.

Question 3. Weight of a body is greater at the equator and less at the polar region.
Answer: False – Weight of a body is minimum at the equator. It is maximum at the poles.
In simple words: An object feels heavier at the Earth's poles and lighter at the equator. This is because the Earth bulges slightly at the equator and spins, causing a small outward force that reduces gravity's effect there.

🎯 Exam Tip: The value of 'g' (acceleration due to gravity) is slightly less at the equator due to two factors: Earth's rotation (centrifugal effect) and its equatorial bulge (greater distance from the center). Therefore, weight, which is \( mg \), is minimum at the equator and maximum at the poles.

Question 4. Turning a nut with a spanner having a short handle is so easy than one with a long handle.
Answer: False – Turning a nut with a spanner having a longer handle is so easy than one with a short handle.
In simple words: It is easier to turn a nut using a spanner with a long handle than with a short one. A longer handle gives you more leverage, making it simpler to apply the turning force.

🎯 Exam Tip: The turning effect of a force (torque) is directly proportional to the perpendicular distance from the pivot point to the line of action of the force. A longer handle increases this distance, requiring less force to produce the same torque.

Question 5. Astronauts are falling freely around the earth due to their huge orbital velocity.
Answer: True
In simple words: Astronauts in orbit are constantly falling towards Earth but moving sideways so fast that they keep missing it. This continuous 'free fall' makes them feel weightless.

🎯 Exam Tip: The feeling of weightlessness in orbit is not due to a lack of gravity, but because both the astronauts and their spacecraft are continually accelerating towards Earth at the same rate, effectively being in a state of free fall.

IV. Match The Following.

Question 1. Match the column A with column B.

🎯 Exam Tip: Understand the core concept of each law: First law (inertia/equilibrium), Second law (F=ma/rate of change of momentum), Third law (action-reaction pairs), and Conservation of Momentum (total momentum constant in isolated system).

V. Assertion And Reasoning.

Question 1. Assertion: The sum of the clockwise moments is equal to the sum of the anticlockwise moments. Reason: The principle of conservation of momentum is valid if the external force on the system is zero.
Answer: (b) If both the assertion and the reason are true, but the reason is not the correct explanation of assertion.
In simple words: The first statement is about balance in turning forces. The second statement is about momentum being conserved if there are no outside pushes or pulls. Both are true physics rules, but the second one doesn't explain the first one.

🎯 Exam Tip: Recognize that while both statements are true physics principles, they relate to different concepts: the assertion describes rotational equilibrium (principle of moments), while the reason describes linear momentum conservation. There is no direct causal link between them.

Question 2. Assertion: The value of 'g' decreases as height and depth increases from the surface of the Earth. Reason: 'g' depends on the mass of the object and the Earth.
Answer: (c) Assertion is true, but the reason is false.
In simple words: It is true that gravity's pull ('g') gets weaker both as you go higher up from Earth and deeper down into it. However, 'g' does not depend on the mass of the object being pulled; it depends only on the mass of the Earth and the distance from its center.

🎯 Exam Tip: The acceleration due to gravity 'g' decreases with both altitude and depth. Crucially, 'g' is independent of the mass of the falling object; it only depends on the mass of the planet and the distance from its center (\( g = \frac{GM}{R^2} \)).

VI. Answer Briefly.

Question 1. Define inertia. Give its classification.
Answer: Inertia is the natural tendency of a body to resist any change in its state of rest or of uniform motion, unless an outside unbalanced force acts on it. It means an object will stay put or keep moving at the same speed and direction unless something pushes or pulls it. There are three types of inertia:
1. Inertia of rest: An object at rest wants to stay at rest.
2. Inertia of motion: An object in motion wants to keep moving.
3. Inertia of direction: An object moving in a certain direction wants to keep going in that direction.
In simple words: Inertia is an object's resistance to change its movement or lack of movement. It comes in three kinds: staying still, keeping moving, or staying in the same direction.

🎯 Exam Tip: Clearly state the definition of inertia. For classification, give each type a name and a one-sentence description or example.

Question 2. Classify the types of force based on their application.
Answer: Based on the direction in which forces act, they can be grouped into two main types:
1. Like parallel forces: These are two or more forces, whether equal or unequal in strength, that act in the same direction and are parallel to each other. For example, two people pushing a box together in the same direction.
2. Unlike parallel forces: These are two or more forces, either equal or unequal in strength, that act in opposite directions but are still parallel to each other. For example, two people pushing a box from opposite sides.
In simple words: Forces can be grouped by how they act. "Like parallel forces" mean they push or pull in the same direction, like two people pushing a car forward. "Unlike parallel forces" mean they push or pull in opposite directions, like two people pushing a door from different sides.

🎯 Exam Tip: When classifying forces, remember that "parallel" refers to their lines of action, and "like" or "unlike" refers to whether they are in the same or opposite directions, respectively.

Question 3. If a 5 N and a 15 N forces are acting opposite to one another. Find the resultant force and the direction of action of the resultant force.
Answer:
Given:
First force \( F_1 = 5 \text{ N} \)
Second force \( F_2 = 15 \text{ N} \)
Since the forces act in opposite directions, the resultant force is found by subtracting the smaller force from the larger force.
Resultant force \( F_{\text{R}} = F_1 - F_2 \)
\( F_{\text{R}} = 5 \text{ N} - 15 \text{ N} = -10 \text{ N} \). The negative sign indicates the direction.
The magnitude of the resultant force is \( 10 \text{ N} \).
The resultant force acts in the direction of the larger force, which is the \( 15 \text{ N} \) force.
In simple words: When two forces push in opposite ways, you find the total force by subtracting the smaller one from the bigger one. The total force will push in the same direction as the bigger original force. In this case, it is \( 10 \text{ N} \) in the direction of the \( 15 \text{ N} \) force.

🎯 Exam Tip: When forces act in opposite directions, always subtract their magnitudes to find the resultant force, and the direction of the resultant force will be the same as that of the larger force.

Question 4. Differentiate mass and weight.
Answer: Mass is a measure of the amount of matter in an object, while weight is the force of gravity acting on that object. Mass remains constant regardless of location, whereas weight changes depending on the gravitational pull of the location. For example, an object's mass is the same on Earth and the moon, but its weight is less on the moon due to weaker gravity. Mass is measured in kilograms (kg), and weight is measured in Newtons (N).
In simple words: Mass is how much material is in something, and it never changes. Weight is how hard gravity pulls on that material, so it changes depending on where you are, like on Earth or the Moon.

🎯 Exam Tip: Highlight the key distinction: mass is scalar (amount of matter), weight is vector (force due to gravity). Emphasize that mass is constant, but weight varies with 'g'.

Question 5. Define the moment of a couple.
Answer: A couple is formed when two forces that are equal in strength, opposite in direction, and parallel to each other are applied at two different points on an object. These forces work together to make the object rotate. The turning effect created by these two forces is called the moment of a couple. It describes the tendency of the couple to cause rotation.
In simple words: A "couple" is two equal forces pushing in opposite directions at different spots on an object. This makes the object spin. The strength of this spin is called the moment of a couple.

🎯 Exam Tip: For a couple, emphasize that the two forces are equal in magnitude, opposite in direction, parallel, and have different lines of action. The moment of a couple is what causes pure rotational motion.

Question 6. State the principle of moments.
Answer: The principle of moments states that if a rigid body is balanced (in equilibrium) under the influence of several forces, the total turning effect caused by forces trying to turn it clockwise is equal to the total turning effect caused by forces trying to turn it anti-clockwise. In simpler terms, for an object to be perfectly balanced, all the forces making it turn one way must be exactly matched by forces making it turn the other way.
In simple words: For an object to stay balanced and not turn, the total turning force in one direction must be exactly the same as the total turning force in the opposite direction.

🎯 Exam Tip: The principle of moments is fundamental for understanding rotational equilibrium. Ensure you define it clearly, stating the equality of clockwise and anticlockwise moments about a pivot point.

Question 7. State Newton's second law.
Answer: Newton's second law states that the force acting on an object is directly proportional to the rate at which its linear momentum changes. This change in momentum always happens in the same direction as the force applied. Simply put, a larger force causes a greater and faster change in an object's movement, and this change follows the direction of the push or pull. This law is often summarized by the formula \( F = ma \), where F is force, m is mass, and a is acceleration.
In simple words: Newton's second law says that when you push or pull an object, it moves faster if you push harder, and it moves in the direction you push. How much faster it moves depends on its mass.

🎯 Exam Tip: Remember that Newton's second law connects force, mass, and acceleration (\( F=ma \)). It also emphasizes that force is the cause of a change in momentum over time.

Question 8. Why a spanner with a long handle is preferred to tighten screws in heavy vehicles?
Answer: A spanner with a long handle is preferred for tightening screws in heavy vehicles because it creates a greater turning effect (torque) with less effort. When the spanner has a long handle, the distance from the point where the force is applied to the fixed pivot point (the nut) is increased. According to the principle of moments, a larger distance for the applied force means a greater turning effect for the same amount of force. This extra leverage helps to apply the significant torque needed to tighten large, heavy-duty screws securely.
In simple words: A long spanner handle makes it easier to tighten tough screws because it gives you more leverage. This means you need less strength to make the screw turn tightly.

🎯 Exam Tip: Link this directly to the concept of torque (moment of force). Torque is calculated as Force \( \times \) Perpendicular Distance. A longer handle increases the perpendicular distance, thus maximizing torque for a given force.

Question 9. While catching a cricket ball the fielder lowers his hands backwards. Why?
Answer: When a fielder catches a cricket ball and lowers their hands backward, they increase the time over which the ball's high speed decreases to zero. By increasing this time, the force of impact on their hands is greatly reduced. Newton's second law tells us that force is related to the change in momentum divided by the time taken. So, a longer time for the momentum to change means a smaller force is felt, which helps prevent injury to the fielder's hands. This technique spreads the impact over a longer duration, reducing the peak force.
In simple words: A cricket fielder moves their hands back when catching a ball to give the ball more time to slow down. This makes the force on their hands less strong, so it does not hurt as much.

🎯 Exam Tip: This is an application of the impulse-momentum theorem (\( F \Delta t = \Delta p \)). By increasing \( \Delta t \) (the time of impact), the force \( F \) experienced by the hands is reduced for the same change in momentum \( \Delta p \).

Question 10. How does an astronaut float in a space shuttle?
Answer: Astronauts inside a space shuttle are not actually floating due to an absence of gravity; instead, they are continuously falling freely around the Earth. The space shuttle itself is also falling around the Earth at the same rate, thanks to its very high orbital velocity. Since both the astronauts and the shuttle have the same acceleration towards Earth, they are under a continuous "free fall" condition. This state, where the relative acceleration between the astronaut and the shuttle is zero, results in the sensation of weightlessness. It is similar to the feeling you would get if you were in a falling elevator.
In simple words: Astronauts "float" in a space shuttle because both they and the shuttle are constantly falling around the Earth at the same speed. This steady fall makes them feel weightless, even though Earth's gravity is still pulling them.

🎯 Exam Tip: Explain that weightlessness in orbit is a result of continuous free fall, not the absence of gravity. The orbital velocity ensures they continually miss the Earth while falling.

VII. Solve The Given Problems.

Question 1. Two bodies have a mass ratio of 3 : 4 The force applied on the bigger mass produces an acceleration of 12 ms². What could be the acceleration of the other body, if the same force acts on it.
Answer:
Given:
Ratio of masses \( m_1 : m_2 = 3 : 4 \)
Let \( m_1 = 3x \) and \( m_2 = 4x \). The bigger mass is \( m_2 \).
Acceleration of bigger mass \( a_2 = 12 \text{ m/s}^2 \)
According to Newton's second law, Force \( F = ma \).
Force acting on \( m_2 \) is \( F_2 = m_2 a_2 \)
\( F_2 = (4x) \times (12 \text{ m/s}^2) = 48x \text{ N} \)
The problem states that the same force acts on the other body, so \( F_1 = F_2 \).
Thus, force acting on \( m_1 \) is \( F_1 = 48x \text{ N} \).
Now, we find the acceleration of \( m_1 \):
\( F_1 = m_1 a_1 \)
\( 48x = (3x) a_1 \)
\( a_1 = \frac{48x}{3x} \)
\( a_1 = 16 \text{ m/s}^2 \)
The acceleration of the other body \( m_1 \) is \( 16 \text{ m/s}^2 \).
In simple words: We have two objects, one is heavier than the other. If the same push is given to both, the lighter object will speed up more than the heavier one. Here, the lighter object (mass ratio 3) will accelerate at \( 16 \text{ m/s}^2 \) compared to the heavier object (mass ratio 4) which accelerates at \( 12 \text{ m/s}^2 \).

🎯 Exam Tip: Remember that force is directly proportional to acceleration and inversely proportional to mass (\( a = F/m \)). If the force is constant, a smaller mass will experience a larger acceleration.

Question 2. A ball of mass 1 kg moving with a speed of 10 ms\(^{-1}\) rebounds after a perfect elastic collision with the floor. Calculate the change in linear momentum of the ball.
Answer:
Given:
Mass of the ball \( m = 1 \text{ kg} \)
Initial speed \( u = 10 \text{ m/s} \)
Since it's a perfect elastic collision, the speed remains the same after rebounding, but the direction reverses. So, the final speed is \( v = -10 \text{ m/s} \).
Initial momentum \( p_{\text{initial}} = mu = 1 \text{ kg} \times 10 \text{ m/s} = 10 \text{ kg m/s} \)
Final momentum \( p_{\text{final}} = mv = 1 \text{ kg} \times (-10 \text{ m/s}) = -10 \text{ kg m/s} \)
Change in momentum \( \Delta p = p_{\text{final}} - p_{\text{initial}} \)
\( \Delta p = (-10 \text{ kg m/s}) - (10 \text{ kg m/s}) \)
\( \Delta p = -20 \text{ kg m/s} \)
The change in linear momentum of the ball is \( -20 \text{ kg m/s} \). The negative sign indicates the change is in the opposite direction to the initial motion.
In simple words: When a ball bounces perfectly, it hits and comes back with the same speed but in the opposite direction. The total change in its moving force (momentum) will be double its original momentum, but in the reverse direction.

🎯 Exam Tip: For elastic collisions, the speed is conserved, but the direction of velocity reverses. When calculating change in momentum, always assign a positive direction to initial velocity and a negative direction to final (rebounding) velocity.

Question 3. A mechanic unscrew a nut by applying a force of 140 N with a spanner of length 40 cm. What should be the length of the spanner if a force of 40 N is applied to unscrew the same nut?
Answer:
Given:
First force applied \( F_1 = 140 \text{ N} \)
Length of the first spanner \( d_1 = 40 \text{ cm} = 40 \times 10^{-2} \text{ m} \)
Second force applied \( F_2 = 40 \text{ N} \)
Let the length of the second spanner be \( d_2 \).
According to the principle of moments, for the same nut (meaning the same required turning effect or torque), the moments must be equal:
\( F_1 \times d_1 = F_2 \times d_2 \)
\( 140 \text{ N} \times (40 \times 10^{-2} \text{ m}) = 40 \text{ N} \times d_2 \)
\( 140 \times 40 = 40 \times d_2 \)
\( d_2 = \frac{140 \times 40}{40} \)
\( d_2 = 140 \text{ cm} = 1.4 \text{ m} \)
The length of the spanner required for the second force is \( 140 \text{ cm} \).
In simple words: If you need to turn a nut with a certain amount of force (torque), and you use less force, you will need a longer spanner handle to get the job done. If you push with less force, you need a longer lever to make it turn.

🎯 Exam Tip: This problem illustrates the inverse relationship between force and the lever arm length (distance) for a constant torque. \( \text{Torque} = F \times d \). If torque is constant, then \( F_1 d_1 = F_2 d_2 \).

Question 4. The ratio of masses of two planets is 2 : 3 and the ratio of their radii is 4 : 7. Find the ratio of their accelerations due to gravity.
Answer:
Given:
Ratio of masses \( m_1 : m_2 = 2 : 3 \)
Ratio of radii \( R_1 : R_2 = 4 : 7 \)
The acceleration due to gravity on a planet is given by the formula \( g = \frac{GM}{R^2} \), where G is the gravitational constant, M is the mass of the planet, and R is its radius.
For planet 1: \( g_1 = \frac{GM_1}{R_1^2} \)
For planet 2: \( g_2 = \frac{GM_2}{R_2^2} \)
To find the ratio \( g_1 : g_2 \), we divide \( g_1 \) by \( g_2 \):
\( \frac{g_1}{g_2} = \frac{\frac{GM_1}{R_1^2}}{\frac{GM_2}{R_2^2}} \)
\( \implies \frac{g_1}{g_2} = \frac{M_1}{R_1^2} \times \frac{R_2^2}{M_2} \)
\( \implies \frac{g_1}{g_2} = \left(\frac{M_1}{M_2}\right) \times \left(\frac{R_2}{R_1}\right)^2 \)
Substitute the given ratios:
\( \frac{M_1}{M_2} = \frac{2}{3} \)
\( \frac{R_2}{R_1} = \frac{7}{4} \)
\( \implies \frac{g_1}{g_2} = \left(\frac{2}{3}\right) \times \left(\frac{7}{4}\right)^2 \)
\( \implies \frac{g_1}{g_2} = \left(\frac{2}{3}\right) \times \left(\frac{49}{16}\right) \)
\( \implies \frac{g_1}{g_2} = \frac{2 \times 49}{3 \times 16} \)
\( \implies \frac{g_1}{g_2} = \frac{98}{48} \)
\( \implies \frac{g_1}{g_2} = \frac{49}{24} \)
Thus, the ratio of their accelerations due to gravity is \( 49 : 24 \).
In simple words: Gravity on a planet depends on its mass and how big it is. If we compare two planets with different masses and sizes, we can calculate how much stronger or weaker gravity is on each. In this case, even though one planet is heavier, the other has a smaller radius, making its gravity stronger.

🎯 Exam Tip: The acceleration due to gravity \( g \) is directly proportional to mass \( M \) and inversely proportional to the square of the radius \( R \). When dealing with ratios, remember to invert the radius ratio if it's \( R_1:R_2 \) and you need \( R_2:R_1 \).

Question 3. Deduce the equation of a force using Newton's second law of motion.
Answer:
Let's consider an object with mass 'm' moving in a straight line with an initial velocity \( V \). After a time period 't', an unbalanced external force 'F' acts on the object, causing its velocity to change to \( v \).
The initial momentum of the body is \( P_{\text{initial}} = m \times V \).
The final momentum of the body is \( P_{\text{final}} = m \times v \).
The change in momentum \( \Delta p = P_{\text{final}} - P_{\text{initial}} = mv - mV = m(v - V) \).
Newton's second law states that force is directly proportional to the rate of change of linear momentum.
So, Force \( F \propto \text{rate of change of momentum} \)
\( \implies F \propto \frac{\text{change in momentum}}{\text{time}} \)
\( \implies F \propto \frac{m(v - V)}{t} \)
We know that acceleration \( a = \frac{\text{change in velocity}}{\text{time}} = \frac{v - V}{t} \).
Substituting 'a' into the proportionality:
\( F \propto ma \)
To convert this proportionality into an equation, we introduce a constant 'k'.
\( F = kma \)
In the SI system of units, the constant \( k \) is equal to 1. This means a unit force produces a unit acceleration in a unit mass.
Therefore, the equation of force is \( F = ma \). This is the mathematical form of Newton's second law, showing that force is equal to mass times acceleration.
In simple words: Newton's second law explains that a push or pull (force) makes an object speed up or slow down (accelerate). The stronger the push and the lighter the object, the more it speeds up. So, Force equals mass times acceleration.

🎯 Exam Tip: Start with the definition of Newton's second law in terms of momentum change. Clearly show the steps, defining initial and final momentum, change in momentum, and how this leads to \( F=ma \).

Question 4. State and prove the law of conservation of linear momentum.
Answer:
**Statement of Law:** The law of conservation of linear momentum states that if no external force acts on a system of two or more interacting objects, their total linear momentum remains constant (conserved). This means that the total momentum before any interaction (like a collision) is equal to the total momentum after the interaction.

**Proof:**
Consider two bodies, A and B, with masses \( m_1 \) and \( m_2 \), respectively. They are moving along a straight line with initial velocities \( u_1 \) and \( u_2 \). Let's assume \( u_1 > u_2 \), so body A will eventually collide with body B.
During the collision, which lasts for a time interval 't' seconds:
Body A exerts a force \( F_A \) on body B.
Body B exerts a force \( F_B \) on body A.
After the collision, the bodies move with final velocities \( v_1 \) and \( v_2 \) along the same straight line.

From Newton's second law, the force is the rate of change of momentum:
Force on body B due to A: \( F_{\text{AB}} = \frac{m_2(v_2 - u_2)}{t} \)
Force on body A due to B: \( F_{\text{BA}} = \frac{m_1(v_1 - u_1)}{t} \)

According to Newton's third law of motion, for every action, there is an equal and opposite reaction. So, the force exerted by A on B is equal in magnitude and opposite in direction to the force exerted by B on A.
Action force \( = - \) Reaction force
\( F_{\text{AB}} = -F_{\text{BA}} \)
\( \implies \frac{m_2(v_2 - u_2)}{t} = -\frac{m_1(v_1 - u_1)}{t} \)
We can cancel 't' from both sides:
\( m_2(v_2 - u_2) = -m_1(v_1 - u_1) \)
\( m_2 v_2 - m_2 u_2 = -m_1 v_1 + m_1 u_1 \)
Rearranging the terms to group initial and final momenta:
\( m_1 u_1 + m_2 u_2 = m_1 v_1 + m_2 v_2 \)
This equation shows that the total momentum before the collision (left side) is equal to the total momentum after the collision (right side). This proof confirms that in the absence of any external force, the total linear momentum of the system is conserved.
In simple words: The law of conservation of momentum means that in a closed group of objects, the total "push" or "movement energy" always stays the same. If two objects bump into each other, their total movement before the bump is the same as their total movement after. This happens because for every push one object gives, it gets an equal and opposite push back.

🎯 Exam Tip: Clearly state the law first, emphasizing the "isolated system" condition. In the proof, correctly apply Newton's second and third laws, and ensure your algebraic steps logically lead to the equality of total initial and final momentum.

Question 5. Describe rocket propulsion.
Answer: Rocket propulsion works based on two main ideas: the law of conservation of linear momentum and Newton's third law of motion. Rockets carry fuel, which can be liquid or solid, in a special tank. When the rocket is launched, this fuel burns, and hot gas shoots out from the back (the nozzle) at a very high speed. This creates a large push, or momentum. To balance this push, an equal and opposite force, called a reaction force, is created inside the engine's burning chamber, which pushes the rocket forward. As the rocket moves, its total mass gets lighter because it uses up its fuel. This leads to a gradual increase in the rocket's speed as it goes higher. Eventually, the rocket reaches a speed called escape velocity, which is fast enough for it to break free from Earth's gravity. This continuous ejection of mass helps the rocket gain speed and move against gravity.
In simple words: Rockets move forward by burning fuel and pushing hot gas out very fast, following Newton's laws of motion. This push creates an equal and opposite reaction that makes the rocket fly.

🎯 Exam Tip: When describing rocket propulsion, always mention both the conservation of linear momentum and Newton's third law as the underlying principles, as they are crucial for a complete answer.

Question 6. State the universal law of gravitation and derive its mathematical expression.
Answer: Newton's universal law of gravitation states that every single particle of matter in the universe pulls every other particle towards itself with a force. This force is directly proportional to the product of their masses, meaning if the masses are larger, the force is stronger. The force is also inversely proportional to the square of the distance between the centers of these masses, meaning if they are further apart, the force quickly becomes much weaker. The direction of this force always acts along the straight line that connects the centers of the two masses. This gravitational force is always attractive and does not depend on what material is between the objects.

**Mathematical Expression:**
Let \( m_1 \) and \( m_2 \) be the masses of two bodies, A and B.
Let \( r \) be the distance between their centers.

According to the law of gravitation:
Force \( F \propto m_1 \times m_2 \) (Directly proportional to the product of masses)
Force \( F \propto \frac{1}{r^2} \) (Inversely proportional to the square of the distance)

Combining these two expressions:
\( F \propto \frac{m_1 m_2}{r^2} \)
To change this proportionality into an equation, we introduce a constant \( G \):
\( F = \frac{G m_1 m_2}{r^2} \)

Here, \( G \) is the universal gravitational constant. Its value in the SI unit system is approximately \( 6.674 \times 10^{-11} \text{ Nm}^2 \text{ kg}^{-2} \). The strength of gravity is often visualized as a field around massive objects, influencing other objects within that field.
In simple words: The law says that all objects with mass pull on each other. This pull is stronger if the objects are heavier and weaker if they are farther apart. The formula \( F = \frac{G m_1 m_2}{r^2} \) calculates this pulling force.

🎯 Exam Tip: When deriving the formula, clearly state the proportionalities first, then combine them, and finally introduce the gravitational constant G. Remember to also define G and its value.

Question 7. Give the applications of gravitation.
Answer: Here are some applications of the law of gravitation:
1. We can measure the sizes of celestial bodies, like the mass and radius of the Earth, and even the acceleration due to gravity with great accuracy. This helps us understand our planet and other planets better.
2. The law helps scientists find new stars and planets in space, as their gravitational pull can affect the motion of other known celestial bodies.
3. It helps explain certain unusual movements of stars, sometimes called 'wobbles'. By studying these wobbles, scientists can figure out the mass of nearby planets that cause these disturbances.
4. Gravitation explains why plant roots grow downwards, a process called geotropism. Roots respond to Earth's gravity and always grow in that direction to find water and nutrients.
5. This law is also used to predict exactly where astronomical bodies will move in space, helping us track planets, moons, and even comets.
In simple words: Gravity helps us measure planets, find new stars, understand why roots grow down, and predict how objects move in space.

🎯 Exam Tip: Focus on distinct applications that showcase the broad impact of gravitation, from planetary motion to everyday phenomena like root growth.

IX. HOT Questions

Question 1. Two blocks of masses 8 kg and 2 kg respectively lie on a smooth horizontal surface in contact with one other. They are pushed by a horizontally applied force of 15 N. Calculate the force exerted on the 2 kg mass.
Answer:
Mass of first block \( m_1 = 8 \text{ kg} \)
Mass of second block \( m_2 = 2 \text{ kg} \)
Total mass \( M = m_1 + m_2 = 8 + 2 = 10 \text{ kg} \)
Force applied \( F = 15 \text{ N} \)
First, find the acceleration of the system:
\( \text{Acceleration } a = \frac{F}{M} \)
\( a = \frac{15}{10} = 1.5 \text{ m/s}^2 \)
Now, calculate the force exerted *on* the 2 kg mass, which is \( m_2 \). This force is what makes \( m_2 \) accelerate.
Force exerted on the 2 kg mass, \( F_2 = m_2 a \)
\( F_2 = 2 \times 1.5 = 3 \text{ N} \)
Therefore, the 8 kg block exerts a 3 N force on the 2 kg block, pushing it forward.
In simple words: When a force pushes two blocks together, both blocks accelerate at the same rate. We first find this acceleration, then use it to figure out how much force the first block pushes on the second, lighter block.

🎯 Exam Tip: For problems involving blocks in contact, always find the common acceleration of the system first. Then, apply Newton's second law to the specific block on which the force is being exerted.

Question 2. A heavy truck and bike are moving with the same kinetic energy. If the mass of the truck is four times that of the bike, then calculate the ratio of their momenta.
Answer:
Let the mass of the truck be \( m_1 \)
Let the mass of the bike be \( m_2 \)
Given: mass of truck \( m_1 = 4m_2 \)
This means \( \frac{m_1}{m_2} = 4 \)
Also given: Kinetic energy of truck \( K.E_1 = K.E_2 \) Kinetic energy of bike
We know the relation between kinetic energy (KE) and momentum (P): \( K.E = \frac{P^2}{2m} \)
So, \( \frac{P_1^2}{2m_1} = \frac{P_2^2}{2m_2} \)
\( \frac{P_1^2}{m_1} = \frac{P_2^2}{m_2} \)
\( \frac{P_1^2}{P_2^2} = \frac{m_1}{m_2} \)
Taking the square root of both sides:
\( \frac{P_1}{P_2} = \sqrt{\frac{m_1}{m_2}} \)
Substitute the given mass ratio:
\( \frac{P_1}{P_2} = \sqrt{4} \)
\( \frac{P_1}{P_2} = 2 \)
Therefore, the ratio of their momenta is \( 2:1 \). This shows that even with the same kinetic energy, a heavier object will have more momentum.
In simple words: Even if a heavy truck and a light bike have the same energy when moving, the truck will have twice as much "moving force" or momentum because it is much heavier.

🎯 Exam Tip: Remember the relationship \( KE = \frac{P^2}{2m} \) for connecting kinetic energy and momentum problems. It's a quick way to solve such ratio questions efficiently.

Question 3. "Wearing helmet and fastening the seat belt is highly recommended for safe journey" Justify your answer using Newton's laws of motion.
Answer: Wearing a helmet and using a seat belt are very important for safety because of Newton's laws of motion:
(i) **Newton's First Law (Inertia) & Second Law:** When a car stops suddenly, the passengers inside continue to move forward due to inertia (Newton's First Law). If they hit the dashboard or windshield, the impact force is very large because their momentum changes very quickly over a short time (Newton's Second Law, \( F = \frac{\Delta P}{\Delta t} \)). A seat belt prevents the person from hitting these hard surfaces. Instead, it applies a force over a longer time, reducing the impact force. Similarly, if a bike rider falls, their head continues to move forward due to inertia. A helmet provides a soft, protective layer that spreads the impact force over a larger area and longer time, reducing the pressure and injury to the head. This extended impact time reduces the overall force.
(ii) **Newton's Third Law:** In a collision, if you hit a surface, that surface will hit you back with an equal and opposite force. For example, if your head hits the road during a fall, the road exerts a large force back on your head. Helmets and seat belts work to reduce the harmful effects of these reaction forces. They either absorb some of the energy or spread the force over a larger area, making it less dangerous. They effectively turn a sharp, damaging impact into a more cushioned, less harmful one.
In simple words: Helmets and seat belts keep you safe by reducing the force of impact during a sudden stop or crash. They do this by making the time of impact longer and spreading the force over a bigger area, which lessens the injury according to Newton's laws.

🎯 Exam Tip: Clearly link each safety measure (helmet, seat belt) to the relevant Newton's laws (inertia, force and momentum change, action-reaction) and explain *how* they reduce injury by increasing impact time or spreading force.

I. Choose the correct answer

Question 1. When a force is exerted on an object, it can change its:
(a) state
(b) shape
(c) position
(d) all the options
Answer: (d) all the options
In simple words: When you push or pull an object, you can make it start moving or stop (change state), squish it (change shape), or move it from one place to another (change position).

🎯 Exam Tip: Remember that force can cause multiple effects, not just motion. Consider all physical changes a force can induce.

Question 2. When the train stops, the passenger moves forward, It is due to
(a) Inertia of passenger
(b) Inertia of train
(c) gravitational pull by the earth
(d) None of the options
Answer: (a) Inertia of passenger
In simple words: When the train stops suddenly, your body wants to keep moving forward because of its inertia, making you lean ahead.

🎯 Exam Tip: This is a classic example of inertia of motion. Always identify which object's inertia is relevant to the observation.

Question 3. Force is a ........ quantity.
(a) vector
(b) fundamental
(c) scalar
(d) none
Answer: (a) vector
In simple words: Force is a vector because it has both a size (how strong it is) and a direction (which way it pushes or pulls).

🎯 Exam Tip: Clearly distinguish between scalar quantities (only magnitude) and vector quantities (magnitude and direction).

Question 4. The force of gravitation is _________.
(a) repulsive
(b) conservative
(c) electrostatic
(d) non-conservative.
Answer: (b) conservative
In simple words: Gravity is a conservative force, which means the work it does on an object only depends on the start and end positions, not on the path taken.

🎯 Exam Tip: Understand that a conservative force, like gravity, allows for the definition of potential energy, which is path-independent.

Question 5. The laws of motion of a body is given by _________.
(a) Galileo
(b) Archimedes
(c) Einstein
(d) Newton
Answer: (d) Newton
In simple words: Isaac Newton is the scientist who gave us the main laws that explain how things move and interact with forces.

🎯 Exam Tip: This is a direct recall question. Be sure to associate key scientific laws with their discoverers.

Question 6. A bodyweight 700 N on earth. What will be its weight on a planet having 1/7 of earth's mass and half of the earth's radius?
(a) 400 N
(b) 300 N
(c) 200 N
(d) 400 N
Answer: (a) 400 N
In simple words: If a body weighs 700 N on Earth, its weight on a planet with 1/7 the Earth's mass and half the Earth's radius will be 400 N. This is because gravity depends on both mass and radius.

🎯 Exam Tip: To solve this, remember the formula for acceleration due to gravity \( g = \frac{GM}{R^2} \) and weight \( W = mg \). Calculate the new 'g' first, then the new weight.
**Calculation:**
Weight on Earth \( W_E = mg_E = 700 \text{ N} \)
\( g_E = \frac{GM_E}{R_E^2} \)
On the new planet:
\( M_P = \frac{1}{7} M_E \)
\( R_P = \frac{1}{2} R_E \)
\( g_P = \frac{GM_P}{R_P^2} = \frac{G (\frac{1}{7} M_E)}{(\frac{1}{2} R_E)^2} = \frac{\frac{1}{7} G M_E}{\frac{1}{4} R_E^2} = \frac{4}{7} \frac{G M_E}{R_E^2} = \frac{4}{7} g_E \)
Weight on planet \( W_P = m g_P = m (\frac{4}{7} g_E) = \frac{4}{7} (m g_E) = \frac{4}{7} W_E \)
\( W_P = \frac{4}{7} \times 700 \text{ N} = 4 \times 100 \text{ N} = 400 \text{ N} \)

Question 7. From the following statements write down that which is not applicable to mass of an object:
(a) It is a fundamental quantity
(b) It is measured using physical balance
(c) It is measured using spring balance
(d) It is the amount of matter.
Answer: (c) It is measured using spring balance
In simple words: Mass is how much 'stuff' an object has and is a basic measurement, found using a physical balance. A spring balance measures weight, not mass.

🎯 Exam Tip: Remember that a physical balance (like a beam balance) compares masses, while a spring balance measures weight, which can change with gravity, unlike mass.

Question 8. Newton's first law of motion defines:
(a) inertia
(b) force
(c) acceleration
(d) both inertia and force
Answer: (d) both inertia and force
In simple words: Newton's first law talks about inertia, which is how objects resist changes in motion, and it also hints at what a force is by saying what happens if there's no net force.

🎯 Exam Tip: Newton's First Law is often called the Law of Inertia, describing an object's tendency to resist changes in its state of motion. It implies the definition of force as an external agent causing such a change.

Question 9. Mechanics is divided into ________ types.
(a) one
(b) two
(c) three
(d) four.
Answer: (b) two
In simple words: The study of how things move and forces work (mechanics) is split into two main parts: statics (things that don't move) and dynamics (things that do move).

🎯 Exam Tip: Recall the two main branches of mechanics: statics (study of forces on objects at rest or in uniform motion) and dynamics (study of forces on objects in motion, considering the cause).

Question 10. When an object undergoes acceleration:
(a) its velocity increases
(b) its speed increases
(c) its motion is uniform
(d) a force always acts on it
Answer: (d) a force always acts on it
In simple words: When an object is accelerating, it means its speed or direction of movement is changing, and this change can only happen if a force is pushing or pulling it.

🎯 Exam Tip: Remember Newton's Second Law, which states that acceleration is directly proportional to the net force and inversely proportional to mass (\( F = ma \)). Thus, acceleration always requires a net force.

Question 11. On what factor does inertia of a body depend?
(a) volume
(b) area
(c) mass
(d) density
Answer: (c) mass
In simple words: Inertia, which is an object's resistance to changing its motion, directly depends on how much mass it has; heavier objects have more inertia.

🎯 Exam Tip: Mass is the fundamental measure of inertia. The more mass an object has, the harder it is to start it moving or stop it once it's in motion.

Question 12. _________ deals with the motion of bodies without considering the cause of motion.
(a) Inertia
(b) Force
(c) Kinematics
(d) kinetics.
Answer: (c) Kinematics
In simple words: Kinematics is the part of science that studies how things move (like speed and distance) without caring about what forces are making them move.

🎯 Exam Tip: Differentiate between kinematics (describes motion) and dynamics (explains motion with forces). This distinction is fundamental in mechanics.

Question 13. If mass of an object is m, velocity v, acceleration a and applied force is F, then momentum P is given by:
(a) \( P = m \times v \)
(b) \( P = m \times a \)
(c) \( P = \frac{m}{v} \)
(d) \( P = \frac{v}{m} \)
Answer: (a) P = m x v
In simple words: Momentum is a measure of how much "oomph" a moving object has, calculated by multiplying its mass by its velocity.

🎯 Exam Tip: This is a definition-based question. Ensure you know the basic formulas for momentum (\( P=mv \)), force (\( F=ma \)), and kinetic energy (\( KE = \frac{1}{2}mv^2 \)).

Question 14. Which of the following is a vector quantity?
(a) speed
(b) distance
(c) momentum
(d) time
Answer: (c) momentum
In simple words: Momentum is a vector quantity because it tells us both how much an object is moving (its magnitude) and in what direction it is moving.

🎯 Exam Tip: Remember that vector quantities have both magnitude and direction (e.g., momentum, velocity, force), while scalar quantities only have magnitude (e.g., speed, distance, time, mass).

Question 15. Unit of momentum in SI system is _________.
(a) ms^-1
(b) Kg ms^-2
(c) Kg ms^-1
(d) ms^-2
Answer: (c) Kg ms^-1
In simple words: Since momentum is mass times velocity, its standard unit is kilograms (for mass) multiplied by meters per second (for velocity).

🎯 Exam Tip: Always derive the unit from the formula (\( P = mv \)), using SI units for each component. \( \text{mass (kg)} \times \text{velocity (m/s)} = \text{kg m/s} \).

Question 16. Force is measured based on:
(a) Newton's first law
(b) Newton's second law
(c) Newton's third law
(d) All the options
Answer: (b) Newton's second law
In simple words: Newton's second law (\( F=ma \)) is the one that actually tells us how to measure force, connecting it to an object's mass and how much it accelerates.

🎯 Exam Tip: While all three laws describe aspects of force, Newton's Second Law (\( F=ma \)) provides the quantitative definition and method for measuring force.

Question 17. Force measures rate of change of:
(a) acceleration
(b) velocity
(c) momentum
(d) distances
Answer: (c) momentum
In simple words: Force directly measures how fast an object's momentum changes over time, as stated by Newton's second law.

🎯 Exam Tip: This is a direct statement from Newton's Second Law: Force is equal to the rate of change of momentum (\( F = \frac{\Delta P}{\Delta t} \)).

Question 18. The rotating or turning effect of a force about a fixed point or fixed axis is called _________.
(a) Force
(b) momentum
(c) torque
(d) couples.
Answer: (c) torque
In simple words: Torque is the turning power of a force that makes an object spin around a central point, like how you turn a doorknob.

🎯 Exam Tip: Distinguish torque from force; force causes linear motion, while torque causes rotational motion. Moment of force is another name for torque.

Question 19. The physical quantity which is equal to the rate of change of momentum is:
(a) displacement
(b) acceleration
(c) force
(d) velocity
Answer: (c) force
In simple words: When an object's momentum changes quickly, it means a strong force is acting on it, so force is directly related to how fast momentum changes.

🎯 Exam Tip: Newton's Second Law in its most general form defines force as the rate of change of momentum. This is a fundamental definition.

Question 20. The momentum of a massive object at rest is:
(a) very large
(b) very small
(c) zero
(d) infinity
Answer: (c) zero
In simple words: Momentum is mass times velocity, so if an object is not moving (velocity is zero), its momentum will also be zero, no matter how heavy it is.

🎯 Exam Tip: Recall the momentum formula \( P = mv \). If velocity (\( v \)) is zero, then momentum (\( P \)) must also be zero, regardless of mass (\( m \)).

Question 21. The velocity which is sufficient to just escape from the gravitational pull of the earth is _________.
(a) drift velocity
(b) escape velocity
(c) gradual velocity
(d) final velocity
Answer: (b) escape velocity
In simple words: Escape velocity is the specific speed an object needs to reach to break free from the gravity of a planet or moon and fly into space without falling back.

🎯 Exam Tip: Escape velocity is a critical concept in space physics, representing the minimum velocity required for an object to overcome the gravitational attraction of a celestial body.

Question 22. A force applied on an object is equal to:
(a) product of mass and velocity
(b) sum of mass and velocity of an object
(c) product of mass and acceleration
(d) sum of mass and acceleration
Answer: (c) product of mass and acceleration
In simple words: The force acting on an object is found by multiplying its mass by its acceleration, which is Newton's second law.

🎯 Exam Tip: This question directly tests Newton's Second Law (\( F = ma \)), which is central to understanding forces and motion.

Question 23. Action and reaction do not balance each other because they:
(a) act on the same body
(b) do not act on the same body
(c) are in opposite direction
(d) are unequal
Answer: (b) do not act on the same body
In simple words: Action and reaction forces don't cancel each other out because they push or pull on two different objects, not just one.

🎯 Exam Tip: A common misconception is that action-reaction pairs cancel. Emphasize that these forces always act on *different* bodies, making cancellation impossible for a single body.

Question 24. The value of variation of acceleration due to gravity (g) is _________ at the centre of the earth.
(a) one
(b) zero
(c) \( \infty \)
(d) \( \frac{1}{\infty} \)
Answer: (b) zero
In simple words: If you could go right to the very center of the Earth, the pull of gravity would be zero because all the mass of the Earth would be pulling you equally in every direction.

🎯 Exam Tip: Remember that inside a uniform spherical shell, gravitational force is zero. At the Earth's center, all mass pulls equally in all directions, leading to a net gravitational acceleration of zero.

Question 25. Action and reaction forces are:
(a) equal in magnitude
(b) equal in direction
(c) opposite in direction
(d) both equal in magnitude and opposite in direction
Answer: (d) both equal in magnitude and opposite in direction
In simple words: Action and reaction forces are always the same strength but always push or pull in exact opposite directions.

🎯 Exam Tip: This directly states Newton's Third Law. It is crucial to remember both aspects: equal magnitude and opposite direction.

Question 26. If mass of a body is doubled then its acceleration becomes:
(a) halved
(b) doubled
(c) thrice
(d) zero
Answer: (a) halved
In simple words: If you double the mass of an object but keep the same pushing force, the object will accelerate only half as much because it's heavier.

🎯 Exam Tip: Apply Newton's Second Law (\( F=ma \)). If force (\( F \)) is constant, then acceleration (\( a \)) is inversely proportional to mass (\( m \)). So, if \( m \) doubles, \( a \) halves.

Question 27. The principle involved in the working of a jet plane is:
(a) Newton's first law
(b) Conservation of momentum
(c) Law of inertia
(d) Newton's second law
Answer: (b) Conservation of momentum
In simple words: Jet planes work by pushing out hot gas in one direction, which makes the plane move in the opposite direction, following the rule that total momentum stays the same.

🎯 Exam Tip: Jet propulsion, like rocket propulsion, is a prime example of the conservation of linear momentum. The expulsion of mass at high velocity in one direction creates momentum, which is balanced by the momentum gained by the plane in the opposite direction.

Question 28. _________ of a body is defined as the quantity of matter contained in the object.
(a) weight
(b) mass
(c) force
(d) momentum.
Answer: (b) mass
In simple words: Mass is simply how much material or 'stuff' an object is made of.

🎯 Exam Tip: Understand that mass is an intrinsic property of an object, representing the amount of matter, and is distinct from weight, which is the force of gravity acting on that mass.

Question 29. A gun gets kicked back when a bullet is fired. It is a good example of Newton's:
(a) first law
(b) first law
(c) second law
(d) third law
Answer: (d) third law
In simple words: When a bullet is fired, it pushes forward, and the gun pushes back on your shoulder with the same force, which is an example of Newton's third law of action and reaction.

🎯 Exam Tip: Recoil of a gun is a classic illustration of Newton's Third Law (action-reaction pairs) and also the conservation of momentum. When the gun exerts a force on the bullet, the bullet exerts an equal and opposite force on the gun.

Question 30. To change the state or position of an object, force is essential.
(a) balanced
(b) unbalanced
(c) electric
(d) elastic
Answer: (b) unbalanced
In simple words: To make something start moving, stop moving, or change its direction, you always need an unbalanced force acting on it. A balanced force results in no change in motion.

🎯 Exam Tip: Remember that balanced forces cause no change in motion, only unbalanced forces can make an object accelerate or change its state.

Question 31. When a bus starts suddenly, the passengers in the standing position are pushed backwards, this action is due to:
(a) first law of motion
(b) second law of motion
(c) third law of motion
(d) conservation of momentum
Answer: (a) first law of motion
In simple words: When the bus suddenly moves, your body wants to stay still because of inertia. This resistance to change in motion makes you feel pushed backward relative to the bus.

🎯 Exam Tip: Newton's first law, also known as the law of inertia, explains why objects resist changes in their state of motion or rest.

Question 32. When a body at rest breaks into two pieces of equal masses, then the parts will move:
(a) in same direction
(b) along different directions
(c) with unequal speeds
(d) in opposite directions with equal speeds
Answer: (d) in opposite directions with equal speeds
In simple words: If something breaks into two equal parts while sitting still, the parts will fly off in exact opposite ways, both moving at the same speed. This is because the total push (momentum) before and after must stay the same.

🎯 Exam Tip: This scenario is a classic example of the conservation of linear momentum, where the total momentum of a system remains constant if no external forces act on it.

Question 33. The principle of function of a jet aeroplane is based on:
(a) first law of motion
(b) second law of motion
(c) third law of motion
(d) all of the options
Answer: (c) third law of motion
In simple words: Jet planes work because they push hot gas backward very fast. As a reaction, the plane gets pushed forward with an equal force.

🎯 Exam Tip: Rocket and jet propulsion are primary real-world applications of Newton's third law, where action and reaction forces drive movement.

Question 34. Which of the following has the largest inertia?
(a) pin
(b) book
(c) pen
(d) table
Answer: (d) table
In simple words: Inertia is how much an object resists changing its motion. Heavier objects have more inertia. A table is usually the heaviest among the choices, so it has the most inertia.

🎯 Exam Tip: Inertia is directly proportional to mass; the more mass an object has, the harder it is to start it moving or stop it from moving.

Question 35. An athlete runs a long path before taking a long jump to increase:
(a) energy
(b) inertia
(c) momentum
(d) force
Answer: (c) momentum
In simple words: Running before a jump helps an athlete gain speed and mass in motion, which increases their momentum. This extra momentum helps them travel a longer distance in the air.

🎯 Exam Tip: Momentum is a crucial concept in sports like long jump, as it directly influences how far an athlete can travel after leaving the ground.

Question 36. The weight of a person is 50 kg. The weight of that person on the surface
(a) 50 N
(b) 35 N
(c) 380 N
(d) 490 N
Answer: (d) 490 N
In simple words: To find the weight of the person on Earth, you multiply their mass (50 kg) by the acceleration due to gravity (about 9.8 m/s²). This calculation gives you 490 Newtons.

🎯 Exam Tip: Always remember the difference between mass (measured in kg) and weight (measured in N), and use \( W = mg \) to calculate weight on Earth where \( g \approx 9.8 \text{ m/s}^2 \).

Question 37. Which is incorrect statement about the action and reaction referred to Newton's third law of motion?
(a) They are equal
(b) They are opposite
(c) They act on the same object
(d) They act on two different objects
Answer: (c) They act on the same object
In simple words: Newton's third law says that for every action, there is an equal and opposite reaction. These forces always act on two different objects, not on the same one.

🎯 Exam Tip: A common mistake is to think action-reaction pairs cancel out because they are equal and opposite, but they can't cancel if they act on different objects.

Question 38. The tendency of a force to rotate a body about a given axis is called:
(a) turning effect of a force
(b) moment of force
(c) torque
(d) all of the options
Answer: (d) all of the options
In simple words: All these words — turning effect of a force, moment of force, and torque — mean the same thing. They all describe how a force can make something spin or twist.

🎯 Exam Tip: These terms are often used interchangeably in physics to describe the rotational effect produced by a force.

Question 39. The moment of force is:
(a) product of force and the perpendicular distance
(b) product of force and velocity
(c) ratio of force to the acceleration
(d) ratio of force to the perpendicular distance
Answer: (a) product of force and the perpendicular distance
In simple words: The moment of force is calculated by multiplying the force by the shortest distance from the pivot point to where the force is applied. This distance must be at a right angle to the force.

🎯 Exam Tip: Always ensure the distance used in the calculation is the perpendicular distance from the pivot to the line of action of the force for an accurate moment of force.

Question 40. If the force rotates the body in the anticlockwise direction, then the moment is called:
(a) clockwise moment
(b) anticlockwise moment
(c) couple
(d) torque
Answer: (b) anticlockwise moment
In simple words: When a force makes something turn against the direction a clock's hands move, we call it an anticlockwise moment. This is a specific way to describe the turning effect.

🎯 Exam Tip: In many physics conventions, anticlockwise moments are considered positive, while clockwise moments are considered negative.

Question 41. Anticlockwise moment is:
(a) positive
(b) negative
(c) opposite
(d) zero
Answer: (a) positive
In simple words: In physics, we usually say that a turning force (moment) that goes against the clock's direction is a positive value. This helps us keep track of direction in calculations.

🎯 Exam Tip: Consistency in sign convention for moments is crucial in problems involving rotational equilibrium or net torque calculations.

Question 42. Clockwise moment or torque is:
(a) zero
(b) always one
(c) negative
(d) positive
Answer: (c) negative
In simple words: Following the common rule in physics, a turning force (moment or torque) that spins something in the same direction as a clock's hands is given a negative sign. This is just a way to show its direction.

🎯 Exam Tip: Understanding the sign convention for moments is key to correctly solving problems involving rotational dynamics and equilibrium.

Question 43. SI unit of moment of force is:
(a) Nm\(^{-2}\)
(b) Nm\(^{-1}\)
(c) Ns
(d) Nm
Answer: (d) Nm
In simple words: Since moment of force is calculated by multiplying force (Newtons) by distance (meters), its standard unit is Newton-meter (Nm). This unit measures how much twisting force is applied.

🎯 Exam Tip: Be careful not to confuse Newton-meter (Nm) for torque with Joules (J) for energy, although they have the same units, they represent different physical quantities.

Question 44. Moment of force produces:
(a) acceleration
(b) linear motion
(c) velocity
(d) angular acceleration
Answer: (d) angular acceleration
In simple words: A moment of force, or torque, is what makes an object start to spin faster or slower. It creates a change in how quickly something rotates, which we call angular acceleration.

🎯 Exam Tip: Just as force causes linear acceleration, torque causes angular acceleration, indicating a change in rotational velocity.

Question 45. Two equal and opposite forces whose lines of action do not coincide are said to constitute a:
(a) couple
(b) torque
(c) unlike force
(d) parallel force
Answer: (a) couple
In simple words: When two forces are exactly the same size but pull in opposite directions, and they are not on the same line, they create a 'couple'. This couple makes an object twist or rotate.

🎯 Exam Tip: A couple is unique because it only produces a rotational effect (torque) and no translational (linear) motion.

Question 46. Couple produces:
(a) translatory motion
(b) rotatory motion
(c) translatory as well as rotatory motion
(d) neither translatory nor rotatory
Answer: (b) rotatory motion
In simple words: A couple of forces always makes an object spin around a point or axis. It does not make the object move in a straight line, only rotate.

🎯 Exam Tip: The net force of a couple is zero, so it cannot cause linear acceleration; its sole effect is to cause angular acceleration or rotation.

Question 47. ....... is an example of couple.
(a) opening or closing a tap
(b) turning of a key in a lock
(c) steering wheel of car
(d) all of the options
Answer: (d) all of the options
In simple words: All these actions involve two forces acting in opposite directions but not on the same line, which creates a twisting motion called a couple. When you turn a tap, key, or steering wheel, you're applying a couple.

🎯 Exam Tip: Common everyday actions like twisting a screwdriver or turning a bicycle handlebar also demonstrate the concept of a couple.

Question 48. Force of attraction between any two objects in the universe is called:
(a) gravitational force
(b) mechanical force
(c) magnetic force
(d) electrostatic force
Answer: (a) gravitational force
In simple words: Gravity is the special force that pulls any two objects together just because they have mass. It's the reason an apple falls from a tree and why planets orbit the sun.

🎯 Exam Tip: Gravitational force is one of the four fundamental forces of nature and always acts as an attractive force between objects with mass.

Question 49. Universal law of gravitation was given by:
(a) Archimedes
(b) Aryabhatta
(c) Kepler
(d) Newton
Answer: (d) Newton
In simple words: Sir Isaac Newton was the scientist who first explained the universal law of gravitation, describing how all objects in the universe attract each other. Kepler's laws described planetary motion, while Newton explained *why* they moved that way.

🎯 Exam Tip: Newton's law of universal gravitation is a foundational concept in physics, explaining phenomena from falling objects to planetary orbits.

Question 50. The force of gravitation between two bodies does not depend on:
(a) product of their masses
(b) their separation
(c) sum of their masses
(d) gravitational constant
Answer: (c) sum of their masses
In simple words: The strength of gravity between two objects depends on how much mass each object has, how far apart they are, and a special number called the gravitational constant. It does not depend on simply adding their masses together.

🎯 Exam Tip: Newton's law of gravitation states that \( F = \frac{Gm_1m_2}{r^2} \), clearly showing dependence on the product of masses, distance squared, and G, but not the sum of masses.

Question 51. Law of gravitation is applicable to:
(a) heavy bodies only
(b) small sized objects
(c) light bodies
(d) objects of any size
Answer: (d) objects of any size
In simple words: The law of gravitation works for all objects, no matter how big or small they are. Everything with mass attracts everything else with mass.

🎯 Exam Tip: The term "universal" in Newton's law of universal gravitation signifies its applicability to all masses, regardless of their size, composition, or location.

Question 52. The value of gravitational constant (G) is:
(a) different at different places
(b) same at all places in the universe
(c) different only at all the places of earth
(d) same only at all the places of earth
Answer: (b) same at all places in the universe
In simple words: The gravitational constant (G) is a special number that is always the same, no matter where you are in the universe. It helps us calculate the force of gravity between any two objects.

🎯 Exam Tip: Unlike 'g' (acceleration due to gravity), which varies with location and altitude, 'G' is a fundamental physical constant with a fixed value.

Question 53. The unit of gravitational constant is:
(a) Nm\(^2\) kg
(b) kgms\(^{-2}\)
(c) Nm\(^2\) kg\(^{-2}\)
(d) ms\(^{-2}\)
Answer: (c) Nm\(^2\) kg\(^{-2}\)
In simple words: The unit for the gravitational constant (G) is Newton meters squared per kilogram squared. This unit comes from the formula for gravitational force, \( F = \frac{Gm_1m_2}{r^2} \).

🎯 Exam Tip: You can derive the unit of G by rearranging the gravitational force formula: \( G = \frac{Fr^2}{m_1m_2} \), which gives \( \frac{\text{N} \cdot \text{m}^2}{\text{kg} \cdot \text{kg}} = \text{Nm}^2\text{kg}^{-2} \).

Question 54. The weight of an object is:
(a) the quantity of matter it contains
(b) its inertia
(c) same as its mass
(d) the force with which it is attracted by the earth
Answer: (d) the force with which it is attracted by the earth
In simple words: Weight is the force of gravity pulling an object towards a planet, usually the Earth. It's different from mass, which is just how much 'stuff' an object has.

🎯 Exam Tip: Weight is a force, so it has direction (always downwards) and is measured in Newtons (N), whereas mass is a scalar quantity measured in kilograms (kg).

Question 55. In vacuum, all freely falling objects have the same:
(a) speed
(b) velocity
(c) force
(d) acceleration
Answer: (d) acceleration
In simple words: If there's no air to slow things down, all objects, no matter how heavy or light, fall with the same increasing speed towards the Earth. This constant rate of speeding up is called acceleration.

🎯 Exam Tip: This principle, famously demonstrated by Galileo, shows that in the absence of air resistance, the acceleration due to gravity 'g' is constant for all falling objects.

Question 56. The acceleration due to gravity:
(a) has the same value everywhere in space
(b) has the same value everywhere on earth
(c) varies with the latitude on earth
(d) is greater on moon due to its smaller diameter
Answer: (c) varies with the latitude on earth
In simple words: The force that pulls things down (gravity) is not exactly the same everywhere on Earth. It changes a little bit depending on how far you are from the equator or the poles.

🎯 Exam Tip: The acceleration due to gravity 'g' varies with latitude because Earth is not a perfect sphere (it bulges at the equator) and due to the Earth's rotation.

Question 57. When an object is thrown up, the force of gravity:
(a) is opposite to the direction of motion
(b) is in the same direction as direction of motion
(c) decreases as it rises up
(d) increases as it rises up
Answer: (a) is opposite to the direction of motion
In simple words: When you throw something into the air, the force of gravity always pulls it downwards. This downward pull goes against the object's upward movement, causing it to slow down.

🎯 Exam Tip: Gravity is a constant downward force near the Earth's surface, acting against upward motion and with downward motion.

Question 58. The SI unit of acceleration due to gravity 'g' is:
(a) ms\(^{-1}\)
(b) ms
(c) ms\(^{-2}\)
(d) ms\(^2\)
Answer: (c) ms\(^{-2}\)
In simple words: The standard way to measure acceleration due to gravity is in meters per second squared. This tells us how much an object's speed changes each second as it falls.

🎯 Exam Tip: The unit for acceleration due to gravity is the same as for any other acceleration, indicating a rate of change of velocity.

Question 59. What happens to the value of 'g' as we go higher from surface of earth?
(a) decreases
(b) increases
(c) no change
(d) zero
Answer: (a) decreases
In simple words: As you go further away from the Earth's surface, the pull of gravity gets weaker. This means the value of 'g' (acceleration due to gravity) becomes smaller at higher altitudes.

🎯 Exam Tip: The acceleration due to gravity is inversely proportional to the square of the distance from the Earth's center, so 'g' decreases with increasing altitude.

Question 60. Mass of a body on moon is:
(a) the same as that on the earth
(b) \( \frac{1}{6} \)th of that at the surface of the earth
(c) 6 times as that on the earth
(d) none of the options
Answer: (a) the same as that on the earth
In simple words: The amount of 'stuff' an object is made of, called its mass, stays the same no matter where it is. So, a body's mass on the Moon is the same as its mass on Earth.

🎯 Exam Tip: Mass is an intrinsic property of an object and is independent of gravity or location, while weight changes depending on the gravitational field.

Question 61. At which place is the value of 'g' is zero?
(a) at poles
(b) at centre of the earth
(c) at equator
(d) above the earth
Answer: (b) at centre of the earth
In simple words: The acceleration due to gravity becomes zero right at the very middle of the Earth. This is because all the gravitational pulls from different parts of the Earth cancel each other out at the center.

🎯 Exam Tip: At the Earth's center, an object would experience weightlessness, as the net gravitational force on it would be zero due to symmetry.

Question 62. The weight of the body is maximum:
(a) at the centre of the earth
(b) on the surface of earth
(c) above the surface of earth
(d) none of the options
Answer: (b) on the surface of earth
In simple words: A body's weight is heaviest right on the surface of the Earth. As you go higher up or deeper down towards the center, the weight decreases because the gravitational pull changes.

🎯 Exam Tip: The maximum value of 'g' (and thus weight) occurs at the Earth's surface, specifically at the poles, due to a combination of distance and Earth's rotation.

Question 63. A rock is brought from the surface of the moon to the earth, then its:
(a) weight will change
(b) mass will change
(c) both mass and weight will change.
(d) mass and weight will remain the same
Answer: (a) weight will change
In simple words: When a rock is moved from the Moon to the Earth, its mass (the amount of material in it) stays the same. However, its weight changes because the Earth has a much stronger gravitational pull than the Moon.

🎯 Exam Tip: Mass is an intrinsic property, while weight is a force that depends on the local gravitational field.

Question 64. Why is the acceleration due to gravity on the surface of the moon is lesser than that on the surface of earth?
(a) because mass of moon is less
(b) radius of moon is less
(c) mass and radius of moon is large
(d) mass and radius of moon is less
Answer: (d) mass and radius of moon is less
In simple words: The Moon has a weaker pull of gravity than Earth because both its total mass and its size (radius) are smaller. The combination of these two factors makes gravity less on the Moon's surface.

🎯 Exam Tip: The formula for acceleration due to gravity is \( g = \frac{GM}{R^2} \), which shows that 'g' depends on both the mass (M) and the radius (R) of the celestial body.

Question 65. If the distance between two bodies is doubled, then the gravitational force between them is:
(a) halved
(b) doubled
(c) reduced to one-fourth
(d) increased by one fourth
Answer: (c) reduced to one-fourth
In simple words: The force of gravity gets weaker very quickly as objects move apart. If you double the distance between them, the gravitational pull becomes four times smaller.

🎯 Exam Tip: Gravitational force follows an inverse square law, meaning it is inversely proportional to the square of the distance between the centers of the two masses.

Question 66. The unit newton can also be written as:
(a) kgm
(b) kgms\(^{-1}\)
(c) kgms\(^{-2}\)
(d) kgm\(^{-2}\)s
Answer: (c) kgms\(^{-2}\)
In simple words: A Newton is the standard unit of force. It can also be expressed as kilograms times meters per second squared, which comes from Newton's second law, Force = mass \( \times \) acceleration.

🎯 Exam Tip: This derived unit for force (kg m/s\(^2\)) is fundamental in understanding the relationship between mass, acceleration, and force.

Question 67. A bus starts for rest and moves after 4 seconds. Its velocity is 100 ms\(^{-1}\). Its uniform acceleration is:
(a) 10 ms\(^{-2}\)
(b) 25 ms\(^{-2}\)
(c) 400 ms\(^{-2}\)
(d) 2.5 ms\(^{-2}\)
Answer: (b) 25 ms\(^{-2}\)
In simple words: The bus starts from still, then reaches a speed of 100 meters per second in 4 seconds. To find how fast it sped up (acceleration), you divide the change in speed by the time taken, which gives 25 meters per second squared.

🎯 Exam Tip: Remember the formula for acceleration, \( a = \frac{v-u}{t} \), where 'v' is final velocity, 'u' is initial velocity, and 't' is time. Starting from rest means \( u = 0 \).

Question 68. A body of mass 10 kg increases its velocity from 2 m/s to 8 m/s within 4 second by the application of a constant force. The magnitude of the applied force is:
(a) 1.5 N
(b) 30 N
(c) 15 N
(d) 150 N
Answer: (c) 15 N
In simple words: First, find how fast the body sped up (acceleration) using the change in velocity over time. Then, multiply this acceleration by the body's mass to find the force that was applied.

🎯 Exam Tip: This problem requires two steps: first calculating acceleration using kinematic equations, and then applying Newton's second law, \( F = ma \), to find the force.

Question 70. Which one of the following is scalar quantity?
(a) momentum
(b) moment of force
(c) speed
(d) velocity
Answer: (c) speed
In simple words: A scalar quantity only has a size (magnitude), but no direction. Speed is scalar because it only tells you how fast something is moving, not where it is going.

🎯 Exam Tip: Distinguish between scalar quantities (like speed, mass, time) and vector quantities (like velocity, momentum, force) which have both magnitude and direction.

Question 71. Which of the following changes the direction of motion of a body?
(a) momentum
(b) force
(c) energy
(d) mass
Answer: (b) force
In simple words: A force is a push or a pull that can make an object speed up, slow down, or change the direction it is moving in. Without a force, an object keeps going in a straight line at a steady speed.

🎯 Exam Tip: Newton's first law of motion states that an object's velocity (which includes direction) changes only if an external force acts on it.

Question 72. When one makes a sharp turns while driving a car he tends to lean sideways due to:
(a) inertia of rest
(b) inertia of motion
(c) inertia of direction
(d) all of the options
Answer: (c) inertia of direction
In simple words: When a car turns sharply, your body wants to keep moving in the original straight line. This resistance to changing direction is called inertia of direction, and it makes you feel like you're leaning sideways.

🎯 Exam Tip: Inertia is an object's resistance to any change in its state of motion, whether that's stopping, starting, or changing direction.

Question 73. The unit of momentum is:
(a) kg m
(b) m/s\(^2\)
(c) kg m/s
(d) joule
Answer: (c) kg m/s
In simple words: Momentum is calculated by multiplying an object's mass (in kilograms) by its velocity (in meters per second). So, its standard unit is kilogram meters per second.

🎯 Exam Tip: Momentum is a vector quantity, meaning it has both magnitude and direction, and its unit reflects both mass and velocity.

Question 74. Moment of a force is given by \( \tau = \)
(a) \( \frac{F}{d} \)
(b) \( F \times 2d \)
(c) \( F \times d \)
(d) \( \frac{F}{d} \)
Answer: (c) \( F \times d \)
In simple words: The twisting power of a force, also known as torque or moment of force, is found by multiplying the size of the force by the perpendicular distance from the pivot point. This formula helps calculate how much an object will rotate.

🎯 Exam Tip: Ensure that 'd' represents the perpendicular distance from the axis of rotation to the line of action of the force; using any other distance will lead to an incorrect calculation.

Question 75. Which of the following work on the principle of torque?
(a) Gears
(b) Seasaw
(c) all of the options
Answer: (c) all of the options
In simple words: Both gears and seesaws use the idea of torque, or twisting force, to work. Gears transfer turning power, and seesaws balance forces around a pivot point to create movement.

🎯 Exam Tip: The principle of moments (or torque) is widely applied in simple machines like levers, wheels and axles, and pulleys to achieve mechanical advantage.

Question 76. The SI unit of gravitational constant
(a) Nm²/g
(b) Nm²kg²
(c) Nm²kg-2
(d) Nmkg
Answer: (c) Nm²kg-2
In simple words: The unit for the universal gravitational constant, often written as G, shows how it relates force, mass, and distance. It helps us calculate the gravitational pull between any two objects.

🎯 Exam Tip: Remember the SI units for fundamental constants like gravitational constant (G) as they are frequently tested in objective questions.

Question 77. What is the value of gravitational constant?
(a) \( 6.674 \times 10^{-11} \) Nm²g-2
(b) \( 9.8 \times 10^{-11} \) Nm²g-2
(c) \( 6.647 \times 10^{-11} \) Nm²g-2
(d) \( 13.28 \times 10^{-11} \) Nm²g-2
Answer: (a) \( 6.674 \times 10^{-11} \) Nm²g-2
In simple words: The gravitational constant (G) is a fixed number used in physics to figure out how strong the gravity is between two objects. It is a very small number, meaning gravity is a weak force unless masses are very large.

🎯 Exam Tip: Memorize the precise value and unit of the universal gravitational constant (G), as small variations can lead to incorrect answers in MCQs.

Question 78. The value of mass of the Earth is:
(a) \( 6.972 \times 10^{24} \) kg
(b) \( 6.792 \times 10^{24} \) kg
(c) \( 5.972 \times 10^{24} \) kg
(d) \( 2.936 \times 10^{24} \) kg
Answer: (c) \( 5.972 \times 10^{24} \) kg
In simple words: The Earth has a very large mass, which is a key factor in how strongly it pulls objects towards its surface due to gravity. This immense mass creates the gravitational field we experience.

🎯 Exam Tip: Keep in mind the approximate values of major physical constants and astronomical data, as they are often required in calculations or multiple-choice questions.

Question 79. At poles of the Earth, weight of the body is:
(a) minimum
(b) maximum
(c) zero
(d) infinity
Answer: (b) maximum
In simple words: A body weighs the most at the Earth's poles because they are slightly closer to the Earth's center and the Earth's rotation has less effect there. This makes the pull of gravity strongest at the poles.

🎯 Exam Tip: Understand that the Earth's shape (bulging at the equator) and rotation influence the effective gravitational acceleration, leading to maximum weight at the poles and minimum at the equator.

Question 80. Where will the value of acceleration due to gravity be minimum?
(a) poles of the earth
(b) centre of the earth
(c) equator of the earth
(d) space
Answer: (d) space
In simple words: The acceleration due to gravity becomes very, very small, almost zero, when you are far away from Earth in space. This is because the gravitational pull lessens greatly with distance.

🎯 Exam Tip: Remember that 'g' is minimum at the Earth's equator (due to centrifugal force and larger radius) compared to poles, and zero at the Earth's center. However, the question asks for the absolute minimum value, which is in space, far from any significant mass.

Question 81. When an elevator is at rest:
(a) Apparent weight is greater than the actual weight
(b) Apparent weight is less than the actual weight
(c) Apparent weight is equal to the actual weight
(d) None of the options
Answer: (c) Apparent weight is equal to the actual weight
In simple words: When an elevator is not moving, the scale inside it will show your normal weight. This is because there is no extra force pushing you up or down.

🎯 Exam Tip: In elevator problems, the apparent weight equals actual weight when the elevator is at rest or moving with constant velocity (zero acceleration).

Question 82. In a lift, apparent weight of a body is equal to zero when the lift is;
(a) moving upwards
(c) moving downwards
(d) falling down freely
Answer: (d) falling down freely
In simple words: If a lift falls without anything stopping it, you would feel weightless inside it. This happens because the lift and everything in it are accelerating downwards at the same rate as gravity.

🎯 Exam Tip: Apparent weight becomes zero (weightlessness) when the elevator is in free fall, meaning its downward acceleration is equal to 'g'.

Question 83. When the lift is moving upward with an acceleration 'a' the apparent weight of the body is:
(a) lesser than actual weight
(b) greater than actual weight
(c) equal to actual weight
(d) zero
Answer: (b) greater than actual weight
In simple words: When an elevator speeds up while going up, you feel heavier than usual. This is because the floor pushes harder on you to make you accelerate upwards along with the lift.

🎯 Exam Tip: When a lift accelerates upwards, the apparent weight is \( W_{apparent} = m(g+a) \), which is greater than the actual weight \( mg \).

Question 84. When an elevator is moving downward, the apparent weight of a person who is in that elevator is:
(a) maximum
(b) zero
(c) minimum
(d) infinity
Answer: (c) minimum
In simple words: When an elevator speeds up while going down, you feel lighter than usual. This is because the floor does not need to push as hard on you to make you accelerate downwards.

🎯 Exam Tip: When a lift accelerates downwards, the apparent weight is \( W_{apparent} = m(g-a) \), which is less than the actual weight \( mg \). If \( a = g \), apparent weight becomes zero.

Question 85. Which law helps to predict the path of the astronomical bodies?
(a) Newton's law of motion
(b) Newton's law of gravitation
(c) Pascal's law
Answer: (b) Newton's law of gravitation
In simple words: Newton's law of gravitation helps us understand and predict how planets and other space objects move around each other. It explains the pull that keeps them in their orbits.

🎯 Exam Tip: Newton's Law of Universal Gravitation is foundational for understanding orbital mechanics and predicting the motion of celestial bodies.

II. Fill In The Blanks

Question 1. To produce a displacement ........ is required.
Answer: force
In simple words: You need a push or a pull, called force, to make something move from its place. Without force, an object will stay where it is.

🎯 Exam Tip: Remember that force is the agent that can cause or change motion (displacement) of an object.

Question 2. Passengers lean forward when the sudden brake is applied in a moving vehicle. This can be explained by ........
Answer: inertia
In simple words: When a moving vehicle stops suddenly, the passengers keep moving forward because of inertia. Inertia is the tendency of objects to keep doing what they are already doing.

🎯 Exam Tip: This phenomenon is a classic example of Newton's First Law of Motion, which describes inertia.

Question 3. By convention, the clockwise moments are taken as ..... and the anticlockwise moments are taken as ........
Answer: negative, positive
In simple words: In physics, turning forces that go clockwise are usually given a minus sign, and those that go counter-clockwise get a plus sign. This helps keep track of their direction.

🎯 Exam Tip: Establish a consistent sign convention (e.g., clockwise negative, anticlockwise positive) when dealing with moments or torques to avoid errors in calculations.

Question 4. ........ is used to change the speed of the car.
Answer: Accelerator
In simple words: The accelerator in a car is the pedal you push to make the car go faster or change its speed. It controls the amount of power from the engine.

🎯 Exam Tip: Identify common tools and their functions in everyday physics contexts to answer such practical questions.

Question 5. A man of mass 100 kg has a weight of ........ at the surface of the Earth.
Answer: \( 980 \text{ N} \)
In simple words: To find a person's weight on Earth, you multiply their mass (how much 'stuff' they are made of) by the force of gravity (about 9.8). So, a 100 kg person weighs 980 Newtons.

🎯 Exam Tip: Always remember the formula for weight: Weight = mass × acceleration due to gravity (W = mg), and use \( g \approx 9.8 \text{ m/s}^2 \).

Question 6. Force: vector then momentum: ......(i)...... ......... Balanced force: resultant of the two forces is zero then......(ii)........ : resultant forces are responsible for change in position or state.
Answer: (i) vector, (ii) imbalanced force
In simple words: Momentum is like force, it also has a direction, making it a vector quantity. When forces on an object do not cancel each other out, they are called unbalanced forces, and these are what cause movement.

🎯 Exam Tip: Clearly distinguish between scalar and vector quantities. Unbalanced forces cause acceleration, while balanced forces result in zero net force and thus no change in motion.

Question 7. Momentum is the product of ........ and ........
Answer: mass, velocity
In simple words: Momentum is calculated by multiplying an object's mass (how much matter it has) by its velocity (how fast it is moving and in what direction). It tells us how much "oomph" a moving object has.

🎯 Exam Tip: The formula for momentum is \( p = mv \). Always remember that momentum is a vector quantity, meaning it has both magnitude and direction.

Question 8. To produce an acceleration of 1 m/s² in an object of mass 1 kg. The force required is ........ and for 3 kg of mass to produce same acceleration, the force required is ........
Answer: 1 N, 3 N
In simple words: If you want to make a 1 kg object speed up by 1 m/s², you need a force of 1 Newton. To make a 3 kg object speed up at the same rate, you would need three times that force, which is 3 Newtons, because force is directly related to mass and acceleration.

🎯 Exam Tip: Apply Newton's Second Law of Motion \( F = ma \). For a constant acceleration, force is directly proportional to mass.

Question 9. Two or more forces are acting in an object and does not change its position, the forces are ........ and it is essential to act some ........ force, to change the state or position of an object.
Answer: balanced, unbalanced
In simple words: If multiple forces act on an object but it stays still, those forces are balanced. To make the object move or change its state, you need an unbalanced force.

🎯 Exam Tip: Balanced forces result in zero net force and no acceleration, while unbalanced forces cause acceleration and a change in the object's state of motion.

Question 10. ......... deals with bodies that are at rest under the action of force.
Answer: Statics
In simple words: Statics is the part of physics that studies objects that are not moving, even when forces are pushing or pulling on them. It looks at how these forces balance out.

🎯 Exam Tip: Distinguish between statics (study of bodies at rest or in equilibrium) and dynamics (study of bodies in motion, considering forces).

Question 11. A branch of mechanics that deals with the motion of the bodies considering the cause of motion is called .........
Answer: kinetics
In simple words: Kinetics is a field of study that looks at how things move and also why they move, focusing on the forces that cause the motion. It answers both "how" and "why" things change their movement.

🎯 Exam Tip: Remember that kinetics focuses on the causes of motion (forces), while kinematics describes motion without considering its causes.

Question 12. If m is the mass of a body moving with velocity v then its momentum is given by ........
Answer: mv
In simple words: An object's momentum is found by multiplying its mass (how much material it has) by its velocity (how fast it is moving). This calculation tells us how much "push" the moving object carries.

🎯 Exam Tip: The formula for linear momentum is \( p = mv \), where 'p' is momentum, 'm' is mass, and 'v' is velocity. This is a fundamental concept in mechanics.

Question 13. A system of forces can be brought to equilibrium by applying .......... in opposite direction.
Answer: equilibriant
In simple words: To make a set of forces balance out, you can add a single force that is equal in strength but points in the exact opposite direction. This added force is called an equilibriant.

🎯 Exam Tip: An equilibriant is a single force that, when added to a system of forces, results in zero net force, bringing the system into equilibrium.

Question 14. Torque is a ......... quantity.
Answer: vector
In simple words: Torque is a turning force, and it is a vector quantity, meaning it has both a strength and a direction (which way it is turning). It tells us how effective a force is at making something spin.

🎯 Exam Tip: Understand that torque, like force, is a vector quantity, as its effect (rotation) has a specific direction.

Question 15. Steering wheel transfers a torque to the wheels with ........
Answer: less effort
In simple words: A steering wheel helps you turn the car's wheels easily because it uses the idea of torque. By giving you a larger turning radius, it allows a small force from your hands to create a large turning effect on the wheels.

🎯 Exam Tip: The steering wheel is an application of the principle of moments or torque, where a larger radius (from the center of the wheel to where you apply force) requires less force to produce the same turning effect.

Question 16. The mathematical form of the principle of moments is ........
Answer: \( F_1 \times d_1 = F_2 \times d_2 \)
In simple words: The principle of moments says that for something to be balanced, the turning force on one side (force times distance) must be equal to the turning force on the other side. This formula helps us calculate those forces.

🎯 Exam Tip: This equation is critical for solving problems involving equilibrium and levers. Ensure you know what each variable represents.

Question 17. Change in momentum takes place in the ........ of ........
Answer: direction, force
In simple words: When an object's momentum changes, it means its speed or direction of movement has changed. This change always happens in the same direction as the force that caused it.

🎯 Exam Tip: Recall Newton's Second Law, which states that the rate of change of momentum is directly proportional to the applied force and occurs in the direction of the force.

Question 18. 1 Newton = ........
Answer: \( 10^5 \) dyne
In simple words: One Newton is a unit of force in the metric system. It is equal to \( 100,000 \) dynes, which is a smaller unit of force.

🎯 Exam Tip: Remember this conversion factor between Newton (SI unit of force) and dyne (CGS unit of force).

Question 19. If a force F acts on a body for a time t's then the impulse is ........
Answer: \( F \times t \)
In simple words: Impulse is what happens when a force pushes on an object for a certain amount of time. You find it by multiplying the force by the time it acts.

🎯 Exam Tip: The impulse-momentum theorem states that impulse (Force × time) is equal to the change in momentum. This is a crucial concept for understanding collisions.

Question 20. 1 kg f = ........
Answer: 9.8 N
In simple words: One kilogram-force (kgf) is a unit that measures weight, or the force of gravity on one kilogram of mass. It is equal to about 9.8 Newtons.

🎯 Exam Tip: Understand that kilogram-force (kgf) is a unit of force, not mass. It represents the weight of 1 kg mass under standard gravity conditions.

Question 21. The force of attraction between two objects is directly proportional to the product of their ... and inversely proportional to the square of the .......... between them.
Answer: masses, distance
In simple words: The force that pulls two objects together (gravity) gets stronger if their masses are bigger, and it gets weaker very quickly if they are farther apart. This is how gravity works in the universe.

🎯 Exam Tip: This is a key statement of Newton's Law of Universal Gravitation. Make sure to recall "product of their masses" and "square of the distance" accurately.

Question 22. The value of g varies with ........ and ........
Answer: altitude, depth
In simple words: The strength of gravity, 'g', changes depending on how high you are above the Earth or how deep you go inside it. It is strongest at the surface and changes as you move away or towards the center.

🎯 Exam Tip: The acceleration due to gravity (g) is not constant; it decreases both as you go higher (altitude) and as you go deeper into the Earth (depth), becoming zero at the Earth's center.

Question 23. The value of gravitational constant is ...... at all places but the value of acceleration due to gravity ........
Answer: same, differs
In simple words: The gravitational constant (G) is always the same everywhere in the universe. However, the acceleration due to gravity (g) changes depending on factors like location and height.

🎯 Exam Tip: Differentiate between the universal gravitational constant (G), which is a fundamental constant, and the acceleration due to gravity (g), which is a local variable.

Question 24. The relation between g and G is ........
Answer: \( g = \frac{GM}{R^2} \)
In simple words: This formula connects the local gravity (g) with the universal gravitational constant (G), the mass of the planet (M), and its radius (R). It shows how a planet's size and mass determine the gravity on its surface.

🎯 Exam Tip: This is the derived expression for acceleration due to gravity, crucial for solving problems involving gravitational fields.

III. State whether the following statements are true or false. Correct the statement if it is false.

Question 1. Newton's first law explains inertia:
Answer: True
In simple words: Newton's first law tells us that objects tend to keep doing what they are doing (staying still or moving steadily) unless a force acts on them. This tendency is called inertia.

🎯 Exam Tip: Newton's First Law is often called the Law of Inertia because it directly describes this property of matter.

Question 2. If a motion depends on force then it is called as natural motion.
Answer: False - If a motion does not depend on force then it is called as natural motion.
In simple words: Natural motion is when something moves on its own without needing a constant push or pull, like a ball rolling until friction stops it. Motion that needs a force to keep it going is not natural motion.

🎯 Exam Tip: Aristotle's concept of "natural motion" contrasted with "violent motion" (requiring an external force). Newton's laws redefined this, stating that uniform motion in a straight line is "natural" and requires no net force.

Question 3. The resistance of a body to change its state of rest or the state of uniform motion is known as inertia of motion.
Answer: True
In simple words: Inertia is an object's natural resistance to any change in its movement, whether it is sitting still or moving at a steady speed. It means objects want to keep doing what they are already doing.

🎯 Exam Tip: Understand that inertia applies to both the state of rest and the state of uniform motion, representing an object's resistance to any change in its velocity.

Question 4. Linear momentum = mass × acceleration.
Answer: False - Linear momentum = mass × velocity
In simple words: Linear momentum is found by multiplying an object's mass by its speed, not by how fast its speed is changing. The formula is mass times velocity.

🎯 Exam Tip: The formula for linear momentum is \( p = mv \), whereas \( F = ma \) is for force. Confusing velocity and acceleration in this context is a common mistake.

Question 5. Two equal force acting in opposite directions are called unlike parallel forces.
Answer: True
In simple words: When two forces are of the same strength but pull in exact opposite directions, and they act along lines that are parallel, they are called unlike parallel forces.

🎯 Exam Tip: Remember the definitions of various force types, especially parallel forces (like and unlike), which are crucial in understanding rotational motion and equilibrium.

Question 6. If the resultant force of three force acting on body is zero then the forces are called balanced forces.
Answer: True
In simple words: If all the forces pushing and pulling on an object add up to nothing, then those forces are considered balanced. This means the object will either stay still or keep moving at a constant speed.

🎯 Exam Tip: Balanced forces imply that the net force on an object is zero, leading to either static equilibrium (at rest) or dynamic equilibrium (constant velocity).

Question 7. Torque is a scalar quantity.
Answer: False - Torque is a vector quantity
In simple words: Torque is a turning force that has both a strength and a direction (like clockwise or counter-clockwise). Because it has direction, it is a vector, not just a scalar quantity that only has strength.

🎯 Exam Tip: Torque is a vector because its effect (rotation) occurs about a specific axis and in a specific direction (clockwise or counter-clockwise), which can be represented by a vector perpendicular to the plane of rotation.

Question 8. Moment of couple = Force × \( \perp \) r distance between line of action of forces
Answer: True
In simple words: The "moment of a couple" describes the turning effect created by two equal and opposite forces. You calculate it by multiplying the force by the shortest distance between their lines of action.

🎯 Exam Tip: The moment of a couple (torque) is calculated as the magnitude of one force multiplied by the perpendicular distance between the lines of action of the two forces. This produces pure rotational motion.

Question 9. Principle of moments states that moment in clockwise direction = Moment in anti clockwise direction.
Answer: True
In simple words: The principle of moments says that for an object to be balanced and not turn, the total turning force in the clockwise direction must be exactly equal to the total turning force in the counter-clockwise direction.

🎯 Exam Tip: This principle is essential for understanding rotational equilibrium, particularly in problems involving levers and balances.

Question 10. 1 Newton = 1 g cm s-2
Answer: False - 1 Newton = 1 kg ms-2
In simple words: One Newton is the force needed to make a 1 kilogram object speed up by 1 meter per second every second. It is not the force needed for a 1 gram object in centimeters.

🎯 Exam Tip: Carefully distinguish between SI units (Newton, kg, m, s) and CGS units (dyne, g, cm, s). 1 Newton = 1 kg m/s², while 1 dyne = 1 g cm/s².

Question 11. Impulse = Change in momentum
Answer: True
In simple words: Impulse is how much a force changes an object's momentum over a period of time. It means a big force for a short time, or a small force for a long time, can cause the same change in an object's movement.

🎯 Exam Tip: This is a direct statement of the impulse-momentum theorem, a fundamental concept in collision analysis.

Question 12. Propulsion of rockets is based Newton's third law of motion and conservation of momentum.
Answer: True
In simple words: Rockets move forward by pushing gas backward very fast. This works because for every action (gas pushed back), there is an equal and opposite reaction (rocket pushed forward). This also keeps the total "movement" of the system the same.

🎯 Exam Tip: Rocket propulsion is an excellent real-world application illustrating both Newton's Third Law (action-reaction pairs) and the Law of Conservation of Linear Momentum.

Question 13. The value of universal gravitational constant is \( 6.674 \times 10^{-11} \) Nm² kg-2
Answer: True
In simple words: The universal gravitational constant, often written as G, has a fixed numerical value of \( 6.674 \times 10^{-11} \) with specific units. This constant is used to calculate the gravitational force between any two objects in the universe.

🎯 Exam Tip: Always remember the exact value and correct units for the universal gravitational constant, G, as it is a crucial constant in physics problems.

Question 14. The relation between g and G is \( g = \frac{Gm}{R^2} \)
Answer: True
In simple words: This formula shows how the acceleration due to gravity (g) on a planet depends on the universal gravitational constant (G), the planet's mass (m), and its radius (R). It means larger, denser planets have stronger gravity.

🎯 Exam Tip: This equation links the local acceleration due to gravity 'g' to the universal gravitational constant 'G', the mass of the celestial body 'M', and its radius 'R'.

Question 15. The value of acceleration due to gravity decreases as the altitude of the body increases.
Answer: True
In simple words: As you go higher above the Earth, the pull of gravity (and thus the acceleration due to gravity) becomes weaker. This is because you are getting farther away from the Earth's center.

🎯 Exam Tip: Gravitational force follows an inverse square law, so 'g' decreases with increasing distance from the center of the Earth (i.e., with increasing altitude).

Question 16. In a 'free fall' motion acceleration of the body is equal to the acceleration due to gravity.
Answer: True
In simple words: When an object is in free fall, it means only gravity is acting on it. So, its acceleration is exactly the same as the acceleration caused by gravity alone, which is 'g'.

🎯 Exam Tip: Free fall is defined as motion under the influence of gravity alone, meaning air resistance and other forces are negligible, and the acceleration is 'g'.

IV. Match The Following

Question 1. Match the column A with column B.