CBSE Class 11 Physics All Chapters Frequently Asked Questions

PHYSICS WORKSHEETS (CLASS XI)

PHYSICS WORKSHEETS (CLASS XI) - FREQUENTLY ASKED QUESTIONS

PHYSICAL WORLD: FUNDAMENTAL FORCES

Name the force which is independent of the laws of fundamental forces in nature.

Answer: Spring force and frictional force.

Which force plays the key role in the large-scale phenomena of the universe?

Answer: The gravitational force.

Out of the strong nuclear force and the weak nuclear force, which exists during beta decay?

Answer: The weak nuclear force.

Write the scientific principle in the following technologies: (i) computer, (ii) rocket propulsion.

Answer: (i) Digital logic. (ii) Newton's laws of motion.

What is the range of the weak nuclear force in the nuclei?

Answer: Extremely short, of the order of \(10^{-16}\) m.

Write the Einstein mass-energy relation.

Answer: \(E=mc^2\)

What is the major contribution of Dr Homi Jehangir Bhabha in physics?

Answer: The cascade process of cosmic radiation (cosmic ray showers).

Write at least one phenomenon that occurs in the microscopic domain.

Answer: Atomic, molecular and nuclear phenomena.

Name two instruments that involve light in their functioning.

Answer: Telescope and microscope.

Write at least two properties of the gravitational force.

Answer: It is a long-range force and it is always attractive in nature.

Write the properties of the nuclear force.

Answer: It is a short-range force and a non-central force.

Name the strongest force in nature.

Answer: The strong nuclear force.

How does the electromagnetic (E.M.) force get its name?

Answer: When charges are in motion they produce both an electric and a magnetic field, which are inseparable; hence the name.

Name the physicists who unified different forces and different domains in nature.

Answer: Oersted and Maxwell (electricity and magnetism).

What is the basic difference between a chemical reaction and a nuclear reaction?

Answer: In a chemical reaction atoms rearrange themselves to form molecules, whereas in a nuclear reaction mass is converted into energy (the nuclei change).

UNITS AND MEASUREMENT

What is a parallactic angle?

Answer: The angle between the two directions along which a planet (or star) is viewed from two points on the earth.

What is the value of the following angles in radians? (i) 1 minute, (ii) 1 second.

Answer: (i) \(2.91\times10^{-4}\) rad; (ii) \(4.85\times10^{-6}\) rad.

Write the relation between the parallax angle, the basis and the large distance.

Answer: \(\theta=\dfrac{b}{D}\), where \(b\) is the basis (distance between the two observation points) and \(D\) is the distance of the object.

Write the values of the following large distances in SI units: (i) 1 A.U., (ii) 1 parsec.

Answer: (i) \(1.496\times10^{11}\) m; (ii) \(3.08\times10^{16}\) m.

What is parallax?

Answer: The change in the apparent position of an object against a background when it is viewed from two different positions (for example, closing the left and right eye alternately).

What are dimensions?

Answer: Dimensions are the exponents (powers) to which the base quantities such as mass, length and time are raised to represent a physical quantity.

Write the dimensions of (i) Planck's constant, (ii) coefficient of viscosity.

Answer: (i) \([ML^2T^{-1}]\); (ii) \([ML^{-1}T^{-1}]\).

Check whether the given equations are dimensionally correct or incorrect: (a) \(K=\tfrac12mv^2+ma\); (b) \(K=m^2v^3\).

Answer: Both are incorrect. In (a), \(\tfrac12mv^2\) has the dimensions of energy but \(ma\) has the dimensions of force, so they cannot be added; in (b), \(m^2v^3\) does not have the dimensions of energy.

Fill in the blank: \(G=6.67\times10^{-11}\ \text{N m}^2\text{kg}^{-2}=\) ........ \(\text{cm}^3\text{s}^{-2}\text{g}^{-1}\).

Answer: \(6.67\times10^{-8}\)

Write the expression for the time period of oscillation of a simple pendulum.

Answer: \(T=2\pi\sqrt{\dfrac{l}{g}}\)

What is accuracy?

Answer: The closeness of the measured value to the true value.

Explain instrumental error.

Answer: The error caused by a manufacturing defect (or faulty calibration) of the instrument.

Write the relation of the relative error for a quantity \(Z=\dfrac{A^aB^b}{C^c}\).

Answer: \(\dfrac{\Delta Z}{Z}=a\dfrac{\Delta A}{A}+b\dfrac{\Delta B}{B}+c\dfrac{\Delta C}{C}\)

In an Ohm's law experiment, \(V=(100\pm5)\) V and \(I=(10\pm0.2)\) A. Find the percentage error in the resistance.

Answer: 7%. (\(\dfrac{\Delta R}{R}=\dfrac{5}{100}+\dfrac{0.2}{10}=0.07\))

Define (i) absolute error, (ii) relative error.

Answer: (i) The difference between the mean value and the observed value. (ii) The ratio of the absolute error to the mean (observed) value.

KINEMATICS: MOTION IN A STRAIGHT LINE

What is a point object?

Answer: An object whose size is much smaller than the distance it covers in a reasonable duration of time.

What does the area under a v-t graph indicate?

Answer: The displacement.

What will be the nature of the x-t graph for a uniform motion?

Answer: A straight line.

Define relative velocity.

Answer: The velocity of an object with respect to (relative to) another object.

Name the quantity whose unit is \(\text{m s}^{-2}\).

Answer: Acceleration.

What does the slope of a v-t graph indicate?

Answer: Acceleration.

Can the earth be regarded as a point object when it is describing its yearly journey around the Sun?

Answer: Yes.

Under what condition is the average velocity equal to the instantaneous velocity?

Answer: In uniform motion (constant velocity).

If the distance travelled by a moving object varies directly as the time, what conclusion can you draw about the nature of the motion?

Answer: The object moves with uniform velocity (uniform speed).

Can a body have a constant speed but varying velocity? If yes, give an example.

Answer: Yes. Uniform circular motion.

Describe the nature of motion represented by the following graph.

Answer: The acceleration is increasing (the slope of the v-t graph keeps increasing).

The position coordinate of a moving particle is given by \(x=6+18t+9t^2\) (x in metres, t in seconds). Its velocity at \(t=2\) s is: (a) 20 m/s, (b) 34 m/s, (c) 54 m/s, (d) 72 m/s.

Answer: (c) 54 m/s. (\(v=\dfrac{dx}{dt}=18+18t=18+36=54\) m/s)

In the following graph, find the total distance and displacement covered by the particle in 8 s.

Answer: Total distance = 80 m; displacement = 0.

From 0 to 4 s the velocity is +10 m/s, so the displacement is +40 m; from 4 s to 8 s the velocity is \(-10\) m/s, so the displacement is \(-40\) m. Distance = 40 + 40 = 80 m; displacement = 40 \(-\) 40 = 0.

The v-t graphs of two objects make angles of \(30^\circ\) and \(60^\circ\) with the time axis. Find the ratio of their accelerations.

Answer: \(\tan30^\circ:\tan60^\circ=1:3\), i.e. 1/3.

Which of the two, velocity or acceleration, decides the direction of motion of a body?

Answer: Velocity.

KINEMATICS: PROJECTILE MOTION

What is a projectile?

Answer: A body moving under the action of gravity alone (after being given an initial velocity).

What is the vertical component of the velocity of a projectile at the highest point?

Answer: Zero.

What factors determine the span of a high jump?

Answer: The initial speed and the angle of projection.

At what angle of projection is the horizontal range maximum?

Answer: \(45^\circ\)

What is the expression for the horizontal range of a horizontally projected body from a height \(h\)?

Answer: \(R=u\sqrt{\dfrac{2h}{g}}\)

A projectile is projected at \(60^\circ\) with a speed of 30 m/s from point O. Find the horizontal and vertical components of velocity at O.

Answer: Horizontal component = \(30\cos60^\circ\) = 15 m/s; vertical component = \(30\sin60^\circ=15\sqrt3\) m/s.

If a body A of mass M is thrown with velocity v at an angle of \(30^\circ\) to the horizontal and another body B with the same speed at an angle of \(60^\circ\) to the horizontal, what will be the ratio of their horizontal ranges?

Answer: 1 : 1 (since \(\sin60^\circ=\sin120^\circ\)).

Find the ratio of the horizontal ranges of two projectiles projected with the same speed, one at an angle \((45^\circ-\theta)\) and the other at \((45^\circ+\theta)\).

Answer: 1 : 1 (both ranges equal \(\dfrac{u^2\cos2\theta}{g}\)).

What is the nature of the trajectory of a projectile projected at an angle \(\theta\) with the horizontal?

Answer: A parabola.

At what angle of projection are the maximum height and the horizontal range equal?

Answer: \(\theta=\tan^{-1}(4)\)

What is the direction of motion of a projectile at the highest point?

Answer: Horizontal.

A cricket ball is hit at \(45^\circ\) to the horizontal with a kinetic energy E. What is its kinetic energy at the highest point?

Answer: E/2.

The equation of a projectile motion is \(y=ax^2+bx\). What are the values of a and b if the angle of projection is \(\theta\) and the speed of projection is u?

Answer: \(a=-\dfrac{g\sec^2\theta}{2u^2}\), \(b=\tan\theta\).

A bomb is released by a horizontally flying aeroplane. What is the trajectory of the bomb?

Answer: A parabola.

A bullet is dropped from a height while another bullet is fired horizontally from the same height. Will they reach the ground at the same time?

Answer: Yes. Both take the time \(t=\sqrt{2h/g}\), because the vertical motion is the same.

LAWS OF MOTION: NEWTON'S LAWS AND FRICTION

Write the units of momentum and impulse.

Answer: Momentum: kg m/s; impulse: N s.

Which physical quantity is found from the area under a force-time graph?

Answer: Impulse.

Which law of motion is involved in rocket propulsion?

Answer: Newton's third law of motion.

Define the coefficient of friction.

Answer: It is the ratio of the force of friction to the normal reaction.

What are the units and dimensions of the coefficient of friction?

Answer: It has no unit and no dimensions.

State Newton's second law of motion.

Answer: The rate of change of momentum is directly proportional to the applied force and takes place in the direction of the force.

State Newton's third law of motion.

Answer: To every action there is an equal and opposite reaction; action and reaction forces occur in pairs and both act at the same instant.

Calculate the force acting on a body whose linear momentum changes from 20 kg m/s to 60 kg m/s in 10 s.

Answer: \(F=\dfrac{60-20}{10}=4\) N.

State the law of conservation of momentum.

Answer: In an isolated system (no external force), the total linear momentum of the system remains conserved.

Define the angle of friction.

Answer: The angle between the normal reaction and the resultant of the force of limiting friction and the normal reaction.

What is the relation between the angle of friction and the angle of repose?

Answer: They are equal.

What happens to the coefficient of friction when the weight of a body is doubled?

Answer: There is no change.

Two objects having different masses have the same momentum. Which one will move faster?

Answer: The object having the lower mass (the lighter one).

A shell of mass 0.010 kg is fired by a gun of mass 5 kg. If the muzzle speed of the shell is 100 m/s, what is the recoil speed of the gun?

Answer: 0.2 m/s. (\(5\times v=0.010\times100\))

What is the angle of friction between two surfaces in contact if the coefficient of friction is \(\sqrt3\)?

Answer: \(\tan\theta=\sqrt3\), so \(\theta=60^\circ\).

Define limiting friction.

Answer: The maximum value of static friction.

State true or false: friction depends on the area of contact between two surfaces.

Answer: False.

Why are fast-moving objects streamlined in shape?

Answer: To reduce friction (air resistance).

Why is it easier to roll than to slide an object?

Answer: Rolling friction is smaller than sliding friction.

Write the SI unit of normal reaction.

Answer: Newton (N).

State true or false: the coefficient of friction depends on the force of friction between two surfaces.

Answer: False. (It depends on the nature of the two surfaces.)

Write the relation between the angle of friction and the coefficient of friction.

Answer: \(\tan\theta=\mu\)

Why do athletic shoes have spikes?

Answer: To increase friction.

Why is it difficult to write over an oily surface?

Answer: Because the friction is smaller.

Plot a curve between F and R for static friction.

Answer: It is an inclined straight line passing through the origin (limiting friction \(F\) against normal reaction \(R\)).

What can you calculate from the curve between F and R for static friction?

Answer: The coefficient of static friction (the slope of the line).

State the law of limiting friction.

Answer: The limiting friction is directly proportional to the normal reaction: \(F\propto R\).

Why is it easier to continue the motion of an object than to start the motion?

Answer: Kinetic friction is smaller than limiting friction.

LAWS OF MOTION: UNIFORM CIRCULAR MOTION

What provides the centripetal force to a satellite revolving around the earth?

Answer: The gravitational force of attraction.

Is centripetal force needed to produce rotation?

Answer: No.

Does the angle of banking depend upon the mass of the vehicle?

Answer: No.

What provides the centripetal force to a car taking a turn on a level road?

Answer: The force of friction between the tyres and the road.

A train moves on a banked circular bend of rails. Which rail will wear out faster?

Answer: Inner rail.

What furnishes the centripetal force for an electron going round the nucleus?

Answer: The electrostatic force of attraction.

For uniform circular motion, does the direction of the centripetal force depend on the sense of rotation?

Answer: No.

A stone is moved along a vertical circle. What is the minimum velocity at the lowest point?

Answer: \(v=\sqrt{5gr}\)

What happens to the speed of a car on a flat level circular road when its mass is increased?

Answer: There is no change (the maximum safe speed does not depend on mass).

Which force provides the necessary centripetal force for a vehicle on a banked circular road?

Answer: The horizontal component of the frictional force and the horizontal component of the normal reaction.

Which force provides the necessary centripetal force for a stone rotated in a circle by a string?

Answer: The tension in the string.

Which force balances the weight of a car on a level road?

Answer: The normal reaction.

What happens to the maximum speed of a car on a flat level circular road when the radius of the road increases?

Answer: It increases (\(v_{max}=\sqrt{\mu_sRg}\)).

Define centripetal force.

Answer: The force directed towards the centre of a circular path, which keeps a body moving in the circle.

What is the maximum speed of a vehicle on a level circular road?

Answer: \(v_{max}=\sqrt{\mu_sRg}\)

WORK, ENERGY AND POWER

Is work a scalar or a vector? Write its SI unit.

Answer: Work is a scalar quantity. Its SI unit is the joule.

State the work-energy theorem.

Answer: The change in kinetic energy of a particle is equal to the work done on it by the net force.

1 kWh = ........ joule.

Answer: \(3.6\times10^6\) J

Give an example where the work done by a force on a body is negative.

Answer: The work done by friction or a viscous force.

Work done by a force = component of the force in the direction of displacement \(\times\) ........

Answer: the magnitude of the displacement.

State true or false: the work done in the motion of a body over a closed loop is zero for every force in nature.

Answer: False. (It is zero only for conservative forces.)

Find the angle between force and displacement when the work done by the force is zero.

Answer: \(90^\circ\)

The momentum of an object is doubled. How does its kinetic energy change?

Answer: The kinetic energy becomes 4 times.

What should be the angle between the force and the displacement for maximum and minimum work?

Answer: Maximum work: \(0^\circ\); minimum (zero) work: \(90^\circ\).

A body of mass 2 kg is at rest at a height of 10 m above the ground. Calculate its potential energy after it has fallen through half of its height.

Answer: \(U=mgh=2\times9.8\times5=98\) J.

What is the elastic potential energy stored in a spring?

Answer: \(\tfrac12kx^2\)

A body is moving along a circular path. How much work is done by the centripetal force?

Answer: Zero.

1 eV = ........ J.

Answer: \(1.6\times10^{-19}\) J

Define a conservative force.

Answer: A force is conservative if the work done by it is independent of the path followed (depends only on the end points).

The work-energy theorem may be considered as the scalar form of Newton's ........ law.

Answer: Second law.

WORK, ENERGY AND POWER: COLLISIONS

Define an elastic collision.

Answer: A collision in which both the total linear momentum and the total kinetic energy are conserved.

What is a head-on collision?

Answer: A collision in which the colliding bodies move along the straight line joining their centres.

State true or false: in an inelastic collision, the final kinetic energy is always less than the initial kinetic energy of the system.

Answer: True usually but not always.

Which physical quantity is conserved in both elastic and inelastic collisions?

Answer: Linear momentum.

When is the exchange of energy maximum during an elastic collision?

Answer: When the two colliding bodies are of equal masses.

State true or false: in an elastic collision of two bodies, the momentum and energy of each body is conserved.

Answer: False. (The total momentum and total energy of the system are conserved, not those of each body.)

A mass m collides with another mass 2m and sticks to it. What is the nature of the collision?

Answer: Perfectly inelastic.

What is the coefficient of restitution for a perfectly elastic collision?

Answer: One.

When a body collides elastically with another body of equal mass (at rest), what happens to the velocities?

Answer: The bodies exchange their velocities.

When a body collide inelastically with another body of equal mass at rest, then what will be the angle between the two bodies after collision?

Answer: \(90^\circ\) for an elastic collision; it is less than \(90^\circ\) for an inelastic collision.

A ball is dropped from a height of 3 m. What is the height up to which the ball will rebound if the coefficient of restitution is 0.5?

Answer: \(h=e^2H=0.25\times3=0.75\) m.

What happens when a very light body in motion collides head-on with a heavy stationary body in an elastic collision?

Answer: The light body is reflected back with almost the same speed, while the heavy body remains (almost) stationary.

A moving body collides with a stationary body. Is it possible for both to be at rest after the collision?

Answer: No, because linear momentum would not be conserved.

A body of mass 5 kg moving with a velocity of 10 m/s collides with another body of mass 20 kg at rest and comes to rest. What is the velocity of the second body?

Answer: 2.5 m/s. (\(5\times10=20\times v\))

Two bodies A and B of masses 100 g and 400 g are moving towards each other with speeds 100 cm/s and 10 cm/s. They suffer a head-on collision and stick together. In which direction will the combined mass move?

Answer: In the direction of motion of A. (Momentum of A = 100 \(\times\) 100 = 10000 g cm/s; of B = 400 \(\times\) 10 = 4000 g cm/s.)

SYSTEM OF PARTICLES AND ROTATIONAL MOTION

Which quantity is analogous to force in rotational motion?

Answer: Torque.

Write the mathematical form of conservation of angular momentum.

Answer: \(I\omega=\) constant.

What precondition is considered for writing the above equation?

Answer: The external torque acting is zero.

What is the SI unit of torque?

Answer: N m.

"The angular acceleration is directly proportional to the torque and inversely proportional to the moment of inertia." Which law is this?

Answer: Newton's second law in rotational motion.

The total external force on a body is zero. What type of equilibrium is expected?

Answer: Translational equilibrium.

The total external torque on a body is zero. What type of equilibrium is expected?

Answer: Rotational equilibrium.

What principle does an acrobat employ for his/her performance?

Answer: Conservation of angular momentum.

What is the velocity of the bottom point of a disc in contact with the surface for ideal rolling motion?

Answer: Zero.

What is constituted when two equal and opposite forces act not along the same line of action?

Answer: A torque (couple).

Which components of torque are to be considered in simple situations of rotational dynamics?

Answer: The components along the axis of rotation.

Under what condition does the centre of mass coincide with the centre of gravity of a body?

Answer: When the gravitational field does not vary from point to point (is uniform).

Is the total torque acting on a system independent of its origin?

Answer: Yes, provided the total external force is zero.

Is the maximum velocity of pure rolling down an incline dependent on mass?

Answer: No.

Which quantity is analogous to mass in rotational motion?

Answer: Moment of inertia.

Express the moment of inertia in terms of the rotational kinetic energy of a body rotating about an axis with unit angular velocity.

Answer: \(I=2K\) (since \(K=\tfrac12I\omega^2\) with \(\omega=1\)).

What is the moment of inertia of a thin circular ring of radius R about an axis perpendicular to its plane passing through its centre?

Answer: \(MR^2\)

Between a ring and a disc of the same mass, which one has the greater moment of inertia about an axis perpendicular to its plane through its centre?

Answer: The ring.

Which theorems help us to find the moment of inertia of symmetrical bodies about different axes?

Answer: The parallel axis theorem and the perpendicular axis theorem.

Name the quantity which is equal to the distance from the axis of a mass point whose mass is equal to the mass of the whole body and whose moment of inertia equals that of the body about the axis.

Answer: Radius of gyration.

What is the SI unit of the moment of inertia?

Answer: kg m\(^2\).

Which quantity is a measure of the rotational inertia of a body?

Answer: Moment of inertia.

What is the dimensional formula of the moment of inertia?

Answer: \([ML^2]\)

Does a change of the axis position change the moment of inertia of the body about that axis?

Answer: Yes.

What is the moment of inertia of a disc about one of its diameters?

Answer: \(\dfrac14MR^2\)

Which theorem helps to find the answer to the above question?

Answer: The perpendicular axis theorem.

What is the moment of inertia of a ring about a tangent to the circle of the ring (in its plane)?

Answer: \(\dfrac32MR^2\)

Which theorem helps to find the answer to the above question?

Answer: The parallel axis theorem.

How does the angular velocity of a body rotating about an axis change when the mass is distributed farther from the axis of rotation?

Answer: It decreases (the moment of inertia increases, and \(I\omega\) is constant).

GRAVITATION

State Newton's law of gravitation.

Answer: Every body attracts every other body in the universe with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between them; the force acts along the line joining the centres of the two bodies.

What will be the effect on the gravitational force if the distance between two objects is reduced to half?

Answer: The gravitational force becomes 4 times.

Write the relationship between g and G.

Answer: \(g=\dfrac{GM_e}{R_e^2}\)

Give the formula for the acceleration due to gravity of the earth at an altitude h when \(h\ll R\).

Answer: \(g'=g\left(1-\dfrac{2h}{R}\right)\)

What is the value of g at the centre of the earth?

Answer: Zero.

Define gravitational potential energy.

Answer: The gravitational potential energy of an object at a point in a gravitational field is the amount of work done in bringing the object from infinity to that point.

Give the formula for the gravitational potential due to the earth.

Answer: \(V(r)=-\dfrac{GM}{r}\)

If \(G=6.67\times10^{-11}\ \text{N m}^2\text{kg}^{-2}\) on the earth, what is the value of G on the surface of the moon?

Answer: It remains the same (G is a universal constant).

Where is the value of g more, at the equator or at the pole?

Answer: At the pole, because the equatorial radius of the earth is greater than the polar radius.

Name the experiment used to determine the value of G.

Answer: Cavendish's experiment.

What is the value of the gravitational potential at infinity?

Answer: Zero.

Give the formula for the percentage decrease in weight of a body at depth d from the surface of the earth.

Answer: \(\dfrac{d}{R}\times100\)

What is the percentage decrease in g at an altitude of 32 km from the surface of the earth?

Answer: About 1% (\(\dfrac{2h}{R}\times100=\dfrac{2\times32}{6400}\times100\)).

A tunnel is made along the diameter of the earth and a body is released from the surface through it. What will be the nature of its motion?

Answer: Simple harmonic motion.

At what depth is the value of g the same as the value of g at an altitude of 20 km?

Answer: 40 km.

Define escape velocity.

Answer: The minimum velocity required for an object to overcome the gravitational pull of the earth and escape from it.

What is the value of the escape velocity of a body of mass 2 kg on the surface of the earth?

Answer: 11.2 km/s (it does not depend on the mass).

State Kepler's second law of planetary motion.

Answer: The areal velocity of a planet revolving around the Sun remains constant.

What is the height of a geostationary satellite from the surface of the earth?

Answer: About 36000 km (about 35800 km).

What is the orbital velocity of a satellite?

Answer: The velocity required to put a satellite into an orbit around the earth.

Define areal velocity.

Answer: The area swept per unit time by the line joining the Sun and the planet.

On which law is Kepler's second law based?

Answer: The law of conservation of angular momentum.

Write the relationship between the escape velocity and the orbital velocity.

Answer: \(v_e=\sqrt2\,v_o\)

What is the sign of the total energy of a satellite in its orbit?

Answer: Negative.

What will be the effect on the time period of revolution of a satellite if the radius of its orbit is doubled?

Answer: It becomes \(2\sqrt2\) times (\(T^2\propto r^3\)).

What will be the value of the escape velocity on the surface of the earth if a body is projected at an angle of \(45^\circ\)?

Answer: 11.2 km/s (it does not depend on the direction of projection).

What will be the effect on the time period of a satellite if its mass is doubled?

Answer: No effect, as the time period is independent of the mass of the satellite.

The total energy of a satellite in orbit is negative. What does it signify?

Answer: The satellite is bound to the earth (held by the attractive gravitational force).

Why does the velocity of a planet increase as it comes closer to the Sun?

Answer: Due to conservation of angular momentum.

If the earth shrinks to half its radius without any change in its mass, what will be the effect on the escape velocity?

Answer: It will become \(\sqrt2\) times (\(v_e=\sqrt{2GM/R}\)).

MECHANICAL PROPERTIES OF FLUIDS

Write Bernoulli's equation.

Answer: \(P+\tfrac12\rho v^2+\rho gh=\) constant.

What is efflux?

Answer: Efflux means outflow (of a fluid through an opening).

On which principle does a venturimeter work?

Answer: Bernoulli's principle.

State the Magnus effect.

Answer: The dynamic lift on a spinning ball due to the pressure difference across it.

Write the formula which gives Torricelli's law.

Answer: \(v=\sqrt{2gh}\)

Write Bernoulli's equation in terms of pressure head, velocity head and gravitational head.

Answer: \(\dfrac{P}{\rho g}+\dfrac{v^2}{2g}+h=\) constant.

State the equation of continuity in fluid dynamics.

Answer: The volume of fluid flowing per second through any cross-section remains constant for a steady flow: \(A_1v_1=A_2v_2\).

Write an expression for the speed of efflux from a closed container in which the pressure above the liquid is P (outside pressure \(P_0\)).

Answer: \(v=\sqrt{2gh+\dfrac{2(P-P_0)}{\rho}}\)

State two limitations of Bernoulli's principle.

Answer: (i) It is not applicable to turbulent flow. (ii) It does not hold in the presence of viscous drag on the fluid.

What is an aerofoil?

Answer: A specially designed solid body (like an aeroplane wing) so that it experiences an upward lift when moving through air.

For a fluid in steady flow, the increase in flow speed at a constriction follows ........ (conservation of mass / Bernoulli's principle).

Answer: Conservation of mass.

For the model of a plane in a wind tunnel, turbulence occurs at a ........ speed than for an actual plane (greater / smaller).

Answer: Greater.

Write any two characteristics of an ideal fluid.

Answer: It is incompressible, non-viscous and has streamlined flow.

State Torricelli's theorem.

Answer: The velocity of efflux through an orifice at a certain depth below the free surface of a liquid is the same as that attained by a body falling freely through the same height.

Why are boats pushed towards each other when they come close to each other?

Answer: The air velocity increases and the pressure decreases in the narrow gap between them, so the higher outside pressure pushes them together.

Write the SI unit of pressure.

Answer: Pascal (Pa).

Is pressure a vector or a scalar quantity?

Answer: A scalar.

Write a formula for the hydrostatic pressure.

Answer: \(P=h\rho g\)

What is the hydrostatic paradox?

Answer: Different volumes of a liquid in differently shaped vessels, filled to the same height, exert the same pressure at the base.

What is gauge pressure?

Answer: The excess pressure over the atmospheric pressure.

What is the pressure exerted by the atmosphere on the surface of the earth?

Answer: \(1.01\times10^5\) Pa.

What is the effect on the pressure in a fluid in the absence of gravity?

Answer: The pressure due to the weight of the fluid is zero.

On which law do hydraulic machines work?

Answer: Pascal's law.

What is the mechanical advantage of a hydraulic lift?

Answer: \(\dfrac{A_2}{A_1}\), the ratio of the areas of the large and small pistons.

Write the dimensional formula of pressure.

Answer: \([ML^{-1}T^{-2}]\)

Force is a vector quantity but pressure (F/A) is a scalar quantity. Why?

Answer: In pressure only the normal component of the force is considered, which acts the same in all directions; pressure has no direction.

\(P=\lim_{\Delta A\to0}\dfrac{F}{A}\). Explain the significance of this.

Answer: The area should be very small, so that the pressure is defined at a point.

The two thigh bones each of cross-sectional area 10 cm\(^2\) support the upper part of a human body of mass 40 kg. Estimate the average pressure sustained by the bones. Take \(g=10\ \text{m s}^{-2}\).

Answer: \(P=\dfrac{F}{A}=\dfrac{40\times10}{20\times10^{-4}}=2\times10^5\) Pa.

The blood pressure in humans is greater at the feet than at the brain. Why?

Answer: Because of the gauge pressure \(h\rho g\) due to the column of blood, where h is the height of the person.

Where is the pressure in excess in a soap bubble, inside or outside?

Answer: Inside.

THERMODYNAMICS

What is an isothermal process?

Answer: A thermodynamic process in which the temperature remains constant.

What is an adiabatic process?

Answer: A thermodynamic process in which no heat enters or leaves the system (\(\Delta Q=0\)).

What is an isochoric process?

Answer: A thermodynamic process in which the volume remains constant.

What is equilibrium temperature?

Answer: The temperature at which there is no exchange of heat among the systems in contact.

What is an isolated system?

Answer: A system in which there is no exchange of energy or matter with the surroundings.

Can the temperature of an isolated system change?

Answer: No. An isolated system exchanges neither heat nor work with its surroundings, so its internal energy (and, at equilibrium, its temperature) stays constant. The temperature changes in an adiabatic process (for example, when a gas is compressed adiabatically), but such a system is insulated, not isolated, because work is exchanged.

Does the internal energy of an ideal gas change in an adiabatic process?

Answer: Yes.

What is the nature of the P-V diagram for an isobaric process?

Answer: A straight line parallel to the volume axis.

Does the internal energy of an ideal gas change in an isothermal process?

Answer: No.

Write the equation which is used in an isothermal process.

Answer: \(PV=\) constant.

What is the significance of the zeroth law of thermodynamics?

Answer: It leads to the concept of temperature.

Write the equation which is used in an adiabatic process.

Answer: \(PV^\gamma=\) constant.

What is the expression for the work done during an isothermal process?

Answer: \(W=2.303\,nRT\log_{10}\dfrac{V_f}{V_i}\)

What is the expression for the work done by a gas during an adiabatic process?

Answer: \(W=\dfrac{nR(T_1-T_2)}{\gamma-1}=\dfrac{P_1V_1-P_2V_2}{\gamma-1}\) (work done by the gas; the work done on the gas is the negative of this).

What is a quasi-static process?

Answer: A process in which the changes in pressure, volume or temperature of the system are infinitesimally small at every stage, so that the system is always in near equilibrium.

What is the first law of thermodynamics?

Answer: \(\Delta Q=\Delta U+\Delta W\): the heat supplied to a system equals the increase in its internal energy plus the work done by it.

Define internal energy.

Answer: The sum of the total kinetic energy and the total potential energy of the molecules of the system.

Does the internal energy depend on the path taken in going from one state to another?

Answer: No, it depends only on the initial and final states.

Write one limitation of the first law of thermodynamics.

Answer: It does not give the direction of the flow of heat.

Is it possible to convert internal energy into work or mechanical energy?

Answer: Yes.

What forbids the complete conversion of heat into work?

Answer: The second law of thermodynamics.

Why is a gas heated on compression?

Answer: Because the work done in compressing the gas increases its internal energy.

Under what ideal condition can the efficiency of a Carnot engine be 100%?

Answer: If the temperature of the sink is 0 K.

Which one among solid, liquid and gas of the same mass at the same temperature has the greatest internal energy and which the least?

Answer: The gas has the greatest internal energy and the solid has the least.

How is the efficiency of a Carnot engine affected by the nature of the working substance?

Answer: It is independent of the nature of the working substance.

What is the second law of thermodynamics?

Answer: Clausius statement: no process is possible whose sole result is the transfer of heat from a colder body to a hotter body. Kelvin-Planck statement: no process is possible whose sole result is the absorption of heat from a reservoir and its complete conversion into work.

An electric heater supplies heat to a system at a rate of 100 W. If the system performs work at a rate of 75 J/s, at what rate is the internal energy of the system increasing?

Answer: 25 J/s. (\(dU=dQ-dW=100-75\))

Heat is being supplied to a system but the system does not perform any external work. Is it possible? If yes, how?

Answer: Yes. If all the heat \(dQ\) supplied is retained by the system as an increase in internal energy (\(dQ=dU\)), the external work done is zero.

Can mechanical work be completely converted into heat? Is the reverse also possible?

Answer: Mechanical work can be completely converted into heat, but heat extracted from a body cannot be completely converted into useful work.

Why can an engine working under isothermal conditions produce no useful work?

Answer: \(\eta=1-\dfrac{T_2}{T_1}\); for an isothermal process \(T_1=T_2\), so \(\eta=0\).

KINETIC THEORY OF GASES

According to the kinetic theory of gases, between two successive collisions a molecule of a gas moves on a (straight line / curved line).

Answer: A straight line.

According to the kinetic theory of gases, the energy of gas molecules is only (potential / kinetic).

Answer: Kinetic.

Boyle's law is applicable for (an adiabatic process / an isothermal process).

Answer: An isothermal process.

The degrees of freedom for a monoatomic gas is (3 / 9).

Answer: 3

Real gases behave as ideal gases at (low temperature and high pressure / high temperature and low pressure).

Answer: High temperature and low pressure.

According to the kinetic theory of gases, all molecules of a gas are (identical / different).

Answer: Identical.

If the temperature of an ideal gas is increased to four times its initial value, how does it affect its rms speed?

Answer: The rms speed doubles (\(c_2=2c_1\)).

Which one is greater, \(C_V\) or \(C_P\)?

Answer: \(C_P\).

At constant pressure the heat given to an ideal gas is used in how many ways?

Answer: Two ways: to increase the internal energy and to do work of expansion.

An isothermal process is (slow / fast).

Answer: Slow.

According to the kinetic theory of gases, the molecules are solid (spherical / cylindrical).

Answer: Spherical.

Can absolute zero temperature be achieved in practice?

Answer: No.

An adiabatic process is (slow / fast).

Answer: Fast.

Calculate the ratio of the rms velocity of molecules of oxygen gas and hydrogen gas at the same temperature.

Answer: 1 : 4. (\(\sqrt{2/32}=1/4\))

Calculate the average kinetic energy of one gram of helium at \(127^\circ\)C.

Answer: 1246.5 J. (\(n=\tfrac14\) mol, \(T=400\) K; \(E=\tfrac32nRT=\tfrac32\times\tfrac14\times8.31\times400\))

What is an ideal gas?

Answer: A gas in which there is no intermolecular interaction.

Write the ideal gas equation.

Answer: \(PV=nRT\)

What is the mean free path of gas molecules?

Answer: The average distance through which a molecule moves freely between two successive collisions.

Define absolute zero temperature.

Answer: The temperature at which all molecular motion ceases.

Which type of collision is assumed in the kinetic theory of gases?

Answer: Perfectly elastic collisions.

Write one point of difference between an ideal gas and a real gas.

Answer: Intermolecular interaction is significant in a real gas, whereas it is negligible in an ideal gas.

At constant temperature, how does the pressure exerted by an ideal gas depend on its volume?

Answer: It is inversely proportional to the volume.

How does the pressure of a gas depend upon its density?

Answer: At constant temperature it is directly proportional to the density.

Why do gases have two specific heat capacities?

Answer: Because gases expand appreciably on heating, so the heat required depends on whether the pressure or the volume is kept constant.

State the relation between \(C_P\) and \(C_V\) for an ideal gas.

Answer: \(C_P-C_V=R\)

Why is there no atmosphere on the moon?

Answer: The rms velocity of the molecules of all the constituent gases of the atmosphere is more than the escape velocity of the moon.

What is the value of \(C_P/C_V\) for nitrogen gas?

Answer: 1.4

Find the dimensions of RT.

Answer: \([ML^2T^{-2}]\) per mole (energy per mole).

If the absolute temperature of an ideal gas is doubled, how will the average kinetic energy of its molecules be affected?

Answer: It will also be doubled.

OSCILLATIONS AND WAVES

What are periodic functions?

Answer: Functions that repeat themselves after a fixed interval of time.

Write at least one function of time which is (i) periodic and (ii) non-periodic.

Answer: (i) \(\sin\omega t+\cos2\omega t+\sin4\omega t\); (ii) \(e^{-\omega t}\).

A particle of mass m vibrates about the origin of an X-axis between the limit points (\(-A\),0) and (A,0). Write the expression for the instantaneous displacement.

Answer: \(x(t)=A\sin(\omega t+\phi)\)

The instantaneous position of a particle executing SHM is \(x(t)=A\sin(\omega t+\phi)\). Write the expressions for the instantaneous velocity and acceleration.

Answer: \(v(t)=\omega A\cos(\omega t+\phi)\) and \(a(t)=-\omega^2A\sin(\omega t+\phi)\).

The instantaneous position of a particle executing SHM along the X-axis is \(x(t)=A\cos(\omega t+\phi)\). Write the expressions for the P.E. and K.E. as functions of time.

Answer: P.E. \(U(t)=\tfrac12kA^2\cos^2(\omega t+\phi)\); K.E. \(K(t)=\tfrac12kA^2\sin^2(\omega t+\phi)\).

What is a reference circle?

Answer: The circle on which a particle moves with uniform angular speed; its projection on a diameter executes SHM.

A particle moves on a circular path of radius A with angular speed \(\omega\). Write the expressions for the x-projection and y-projection of the radius vector of the rotating particle.

Answer: \(x(t)=A\cos(\omega t+\phi)\) and \(y(t)=A\sin(\omega t+\phi)\).

Plot the corresponding reference circle, assuming the sense of rotation anticlockwise, for \(x=2\sin\left(2\pi t+\dfrac{\pi}{4}\right)\).

Answer: The reference circle has radius 2 m; the particle rotates anticlockwise with angular speed \(2\pi\) rad/s, and at \(t=0\) the radius vector makes an angle \(\pi/4\) (measured from the y-axis for a sine form) with its reference line. The x-projection is \(2\sin(2\pi t+\pi/4)\). (The figure in the source is not legible.)

The figure shows the circular motion of a particle having initial position P at the left end of the horizontal diameter (\(t=0\)), radius 2 m, moving anticlockwise. Write the expression for the x-projection of the radius vector.

Answer: \(x=-2\cos(\omega t)\) (in metres), where \(\omega\) is the angular speed. (The numerical value of \(\omega\) is not legible in the source.)

A particle moves on a uniform circular path of radius A with constant angular speed \(\omega\). Give the direction of the instantaneous velocity and instantaneous acceleration.

Answer: The velocity is along the tangent; the acceleration is directed towards the centre.

Write the expression of a travelling wave in which the particles oscillate along the y-axis and the wave travels along the x-axis.

Answer: \(y(x,t)=A\sin(kx-\omega t)\) or \(y(x,t)=A\cos(kx-\omega t)\).

What is the principle of superposition of waves?

Answer: The net displacement of the resultant wave is the vector sum of the displacements of the individual waves.

A transverse harmonic wave on a long stretched string is represented by \(y(x,t)=3.0\sin\left(36t+0.018x+\dfrac{\pi}{4}\right)\). What are its amplitude and initial phase?

Answer: Amplitude = 3.0 cm; initial phase = \(\pi/4\).

Which of the following is a stationary wave and which a travelling wave? (i) \(y=2\cos3x\sin\omega t\); (ii) \(y=3\sin(5x+0.5t)+4\cos(5x+0.5t)\).

Answer: (i) Stationary wave; (ii) travelling wave.

Explain reflection of waves at (i) a rigid boundary, (ii) at a point fastened on the rod.

Answer: (i) At a rigid boundary the reflected wave undergoes a phase reversal of \(\pi\) (the displacement at the boundary is always zero, so there is a node). (ii) For a point fastened on the rod: see article 15.6 of the NCERT Class XI book.

NAME OF THE CHAPTER : PHYSICAL WORLD

NAME OF THE TOPIC : FUNDAMENTAL FORCES

NAME OF THE CHAPTER : PHYSICAL WORLD

NAME OF THE TOPIC : FUNDAMENTAL FORCES

2. What is the major contribution of DrHomi Jahangir Bhaba In physics?

3. Write one phenomenon (at least one) that occurs in microscopic domain in classical physics.

NAME OF THE CHAPTER : PHYSICAL WORLD

NAME OF THE TOPIC : FUNDAMENTAL FORCES

Q.NO.1 Write the properties of nuclear force.

ANSWERS:

1. Short range and non central force.