ICSE Class 9 Physics Sample Paper with Solutions Set 01

SECTION A (40 Marks)

Attempt all Questions from this Section

Question 1

(i) A simple pendulum is taken from earth to an altitude. Its time period will [1 Mark]
a) Remain unchanged
b) increase
c) decrease
d) Becomes infinite

Answer: (b) increase

The time period \( T \) is inversely proportional to the square root of acceleration due to gravity, i.e., \( T \propto \frac{1}{\sqrt{g}} \). At an altitude, the value of \( g \) decreases. Hence, the value of \( T \) increases.

Teacher's Note:
a) Remember that time period depends directly on length and inversely on acceleration due to gravity.\n b) Students often confuse acceleration due to gravity increasing with altitude, but it always decreases as we go above the earth's surface.

(ii) The mass of the earth is \( 5.97 \times 10^{24} \text{ kg} \). Its order of magnitude will be [1 Mark]
a) 25
b) \( 10^{24} \nonumber \)
c) 24
d) \( 10^{25} \)

Answer: (d) \( 10^{25} \)

Since the numerical value \( 5.97 \gt 3.2 \), the number is rounded to the next power of 10. Thus, Order of magnitude = \( 10^{1} \times 10^{24} = 10^{25} \).

Teacher's Note:
a) To find order of magnitude, express the number in standard form \( M \times 10^{n} \) where \( 1 \le M \lt 10 \).\n b) If \( M \gt 3.162 \), add 1 to the exponent \( n \) to find the correct order of magnitude.

(iii) The SI unit for velocity is [1 Mark]
a) km/h
b) m/s
c) cm/min
d) none of the above

Answer: (b) m/s

The SI unit of displacement is meter (m) and time is second (s), making the SI unit of velocity meters per second (m/s).

Teacher's Note:
a) Always distinguish between CGS, FPS, and SI units in mechanics.\n b) km/h is a practical unit, not the fundamental SI unit.

(iv) The area enclosed by velocity-time graph and the time axis will be equal to the magnitude of [1 Mark]
a) Retardation
b) Displacement
c) Acceleration
d) Speed

Answer: (b) Displacement

Displacement = Velocity \times Time. Therefore, the area under a velocity-time graph represents displacement.

Teacher's Note:
a) Slope of a velocity-time graph gives acceleration, whereas the area under it gives displacement.\n b) Read the axes carefully before concluding whether it is a displacement-time or velocity-time graph.

(v) Assertion: The unit of speed can be expressed in terms of unit of length and time.
Reason: Speed is considered as one of the basic or fundamental units. [1 Mark]
a) Both A and R are true and R is the correct explanation of A
b) Both A and R are true and R is not the correct explanation of A
c) Assertion is false but reason is true.
d) Assertion is true reason is false.

Answer: (d) Assertion is true reason is false.

The assertion is true because speed is defined as distance divided by time, so its units are derived from length and time units. The reason is false because speed is a derived physical quantity, not a fundamental unit.

Teacher's Note:
a) Fundamental quantities are independent physical quantities like mass, length, and time.\n b) Derived quantities depend on fundamental quantities for their units.

(vi) A child on a cart with wheels throws a sandbag forward. As a result: [1 Mark]
a) He moves forward
b) He moves to the right
c) He moves to the left
d) He moves backward

Answer: (d) He moves backward

According to Newton's third law of motion, the sandbag thrown forward exerts an equal and opposite reaction force, causing the cart and child to move backward.

Teacher's Note:
a) Action and reaction forces act on two different bodies.\n b) Throwing an object forward imparts a backward momentum to the person throwing it.

(vii) Identify the contact force among the following. [1 Mark]
a) Electric force
b) Magnetic force
c) Tension force applied through string
d) Gravitational force

Answer: (c) Tension force applied through string

Tension force requires physical contact via a string or medium, making it a contact force, whereas electric, magnetic, and gravitational forces are non-contact field forces.

Teacher's Note:
a) Contact forces arise when two bodies physically touch each other.\n b) Field forces act over a distance without physical contact.

(viii) When a fireman directs a powerful stream of water on a fire from a hosepipe, the hosepipe tends to go backward. This is due to: [1 Mark]
a) Newton's 3rd law
b) Law of conservation of charges
c) Law of conservation of energy
d) Law of Inertia

Answer: (a) Newton's 3rd law

Water rushing out forward with high momentum exerts an equal and backward reaction force on the hosepipe according to Newton's third law.

Teacher's Note:
a) Every action has an equal and opposite reaction.\n b) Rocket propulsion and recoil of a gun work on the exact same principle.

(ix) The normal atmospheric pressure is [1 Mark]
a) 76 m of Hg
b) 76 cm of Hg
c) 76 Pascal
d) 76 mm of Hg

Answer: (b) 76 cm of Hg

Normal atmospheric pressure at sea level supports a mercury column of height 76 cm or 760 mm.

Teacher's Note:
a) Be careful with units: 76 cm equals 760 mm, not 76 mm.\n b) In Pascals, standard atmospheric pressure is approximately \( 1.013 \times 10^5 \text{ Pa} \).

(x) Why does the body of a deep-sea fish burst on bringing her above the sea level? [1 Mark]
a) The atmospheric pressure above the sea level is higher than inside the sea.
b) The atmospheric pressure above the sea level is lower than inside the sea.
c) The body of fish contains dissolved oxygen at much higher pressure than the atmospheric pressure.
d) The body of fish contains dissolved oxygen at much lower pressure than the atmospheric pressure.

Answer: (c) The body of fish contains dissolved oxygen at much higher pressure than the atmospheric pressure.

Deep-sea fish are adapted to withstand extremely high hydrostatic pressures. When brought up, the internal body pressure immensely exceeds the reduced external atmospheric pressure, causing it to burst.

Teacher's Note:
a) Pressure increases with depth in liquids due to weight of the water column above.\n b) Internal and external pressure must remain balanced for structural integrity of biological organisms.

(xi) What will be the weight of a body on the Moon if it weighs 48 N on the Earth? [1 Mark]
a) 48 N
b) 8 N
c) 9.8 N
d) 98 N

Answer: (b) 8 N

Weight on the Moon is one-sixth of its weight on the Earth. \( W_m = \frac{1}{6} \times 48 \text{ N} = 8 \text{ N} \).

Teacher's Note:
a) Mass remains constant everywhere, but weight varies because acceleration due to gravity varies.\n b) Moon's gravity is approximately \( 1/6 \text{th} \) of Earth's gravity.

(xii) A combination of wood and iron, just floats in the water at room temperature. Explain what you will observe when the water is heated. [1 Mark]
a) The combination will still float with the same position.
b) The combination will float on the surface of the liquid.
c) The combination will sink
d) None of the above

Answer: (c) The combination will sink

When water is heated, its density decreases, causing the upthrust acting on the body to reduce. As upthrust becomes less than the weight of the combination, it sinks.

Teacher's Note:
a) Upthrust depends directly on the density of the liquid.\n b) Heating liquids causes expansion, lowering their density and reducing buoyant force.

(xiii) When a solid body is fully immersed in a liquid, the volume of the displaced liquid is [1 Mark]
a) Less than the volume of the solid body.
b) Depends on the manner in which the body is being immersed in the liquid.
c) Greater than the volume of the solid body.
d) Equal to the volume of the solid body.

Answer: (d) Equal to the volume of the solid body.

According to Archimedes' principle, when a solid body is completely immersed, it displaces a volume of liquid exactly equal to its own volume.

Teacher's Note:
a) Immersed volume equals object volume only when fully submerged.\n b) For floating bodies, volume of displaced liquid equals only the immersed portion's volume.

(xiv) The increase in the concentration of carbon dioxide due to human activities is responsible for _____ increase in greenhouse effect. [1 Mark]
a) 60%
b) 10%
c) 35%
d) 5%

Answer: (a) 60%

Carbon dioxide is the primary greenhouse gas contributing roughly 60 percent to the enhanced global greenhouse effect.

Teacher's Note:
a) Memorize the percentage contributions of major greenhouse gases like carbon dioxide, methane, and CFCs.\n b) Carbon dioxide emissions primarily result from fossil fuel combustion and deforestation.

(xv) According to the new cartesian sign convention, [1 Mark]
a) Focal length of both, convex and concave mirror is positive.
b) Focal length of the convex mirror is negative and that of the concave mirror is positive.
c) Focal length of both, convex and concave mirror is negative.
d) Focal length of the convex mirror is positive and the concave mirror is negative.

Answer: (d) Focal length of the convex mirror is positive and the concave mirror is negative.

The principal focus of a concave mirror lies in front of it (left side), giving it a negative focal length, whereas a convex mirror's focus lies behind it (right side), giving it a positive focal length.

Teacher's Note:
a) All distances are measured from the pole of the mirror as the origin.\n b) Directions along the incident light are taken as positive, and against incident light as negative.

Question 2

(i) Fill in the blanks: [5 Marks]
a) A hydraulic jack is based on __________ [Pascal's/Archimedes/Buoyancy] principle.
b) The error induced by wear and tear of screw of a screw gauge is called __________.
c) The focal length of a spherical mirror is __________ [equal to /half of/zero compared to] its radius of curvature.
d) A __________ is a special type of hydrometer to measure the purity of milk
e) The magnetic field lines of earth are __________ [normal/parallel/close] to earth's surface near the magnetic poles and __________ [normal/parallel/close] to earth's surface near the magnetic equator.

Answer:
a) Pascal's
b) Backlash error
c) half of
d) lactometer
e) normal, parallel

Teacher's Note:
a) Backlash error occurs due to wear of threads in mechanical instruments like screw gauges and spherometers.
b) Earth's magnetic field lines emerge perpendicularly at the magnetic poles and run parallel to the surface near the equator.

(ii) A polythene piece is rubbed with wool as a result of which it acquires a negative charge. Will there be any exchange of mass between the wool and the polythene? [2 Marks]

Answer:
Yes, there will be an exchange of mass between the wool and the polythene because electrons are transferred from the wool to the polythene and electrons carry very small but finite mass.

Teacher's Note:
a) Mass of an electron is \( 9.1 \times 10^{-31} \text{ kg} \), which is very small but not zero.
b) Charging by friction involves transfer of electrons, hence a negatively charged body gains a tiny amount of mass.

(iii) A stone is dropped from a top of tower 50 m high. How long will it take to fall to the foot of the cliff? [2 Marks]

Answer:
Given: Distance \( s = 50 \text{ m} \), initial velocity \( u = 0 \), acceleration \( a = g = 9.8 \text{ m/s}^2 \).
Applying second equation of motion, \( s = ut + \frac{1}{2}at^2 \):
\( 50 = 0 + \frac{1}{2} \times 9.8 \times t^2 \)
\( 50 = 4.9 t^2 \)
\( t^2 = \frac{50}{4.9} = 10.2 \)
On solving, we get, \( t = 3.19 \text{ s} \).

Teacher's Note:
a) Always write down the given parameters with proper SI units before selecting the kinematic equation.
b) Since initial velocity is zero, the term \( ut \) becomes zero, simplifying the calculation.

Question 3

(i) Observe the diagram (A) and (B) and answer the following questions based on them:
What does the diagram (A) represent? Define it. [2 Marks]

[Figure: Vernier calipers showing main scale and vernier scale with the vernier zero mark to the right of the main scale zero mark, indicating a positive zero error.]

Answer:
Diagram (A) represents positive zero error.
Definition: Zero error is said to be positive when the zero mark of the vernier scale is to the right of the zero mark of the main scale when both jaws are brought in contact.

Teacher's Note:
a) Positive zero error must be subtracted from the observed reading during measurements.
b) Always check the alignment of the zero marks before taking any reading with vernier calipers.

(ii) Two simple pendulums A and B have equal lengths bet their bobs masses are 75 g and 125 g respectively. What would be the ratio of their time periods? Give reason for your answer. [2 Marks]

Answer:
The ratio of their time periods will be 1 : 1.
Reason: The time period of a simple pendulum is independent of the mass of its bob, depending only on its length and acceleration due to gravity.

Teacher's Note:
a) Formula \( T = 2\pi\sqrt{l/g} \) does not contain mass term \( m \).
b) Changes in mass or material of the bob do not affect the frequency or time period of oscillation.

(iii) Name two substances which expand on heating. [2 Marks]

Answer:
1. Brass
2. Iron
(Other acceptable answers: Copper, Aluminum, Glass, etc.)

Teacher's Note:
a) Most solids undergo thermal expansion when heated due to an increase in average intermolecular separation.
b) Invar is a notable alloy that exhibits very minimal thermal expansion.

(iv) Draw a velocity-time graph when the velocity remains constant. [2 Marks]

Answer:
When the velocity remains constant, the velocity-time graph is a straight line parallel to the time axis.

[Figure: A line graph with Time (s) on the horizontal axis and Velocity (m/s) on the vertical axis, showing a horizontal straight line parallel to the time axis.]

Teacher's Note:
a) A horizontal line parallel to the time axis indicates zero acceleration.
b) Label both axes clearly with physical quantities and units.

(v) What is the source of tension in a string on an atomic scale? [2 Marks]

Answer:
The source of tension in a string on an atomic scale is the inter-atomic restoring force between the molecules of the material.

Teacher's Note:
a) When a string is stretched, atoms are pulled slightly apart beyond their equilibrium separation.
b) Inter-atomic attractive forces resist this displacement, manifesting macroscopically as tension.

(vi) A long metal rod is bent to form a ring with a small gap. If this is heated, will this gap increase or decreases? [2 Marks]

Answer:
The gap will increase because the metal rod expands on heating in all directions, causing the linear dimensions and hence the gap to expand.

Teacher's Note:
a) Thermal expansion causes all parts of an object to expand proportionally, not just outward.
b) Holes and gaps in expanding bodies enlarge just like the solid material surrounding them.

(vii) Why do birds puff up their feathers in winter? [2 Marks]

Answer:
Birds puff up their feathers in winter to trap a large amount of air. Since trapped air is a bad conductor of heat, it prevents body heat from escaping into the cold surroundings, keeping them warm.

Teacher's Note:
a) Trapped air acts as an excellent thermal insulator.
b) Animals use similar adaptations like thick fur or blubber to survive sub-zero temperatures.

Attempt any four Questions from this Section.

Question 4

(i) Define pitch of a screw gauge. The thimble of a screw gauge has 50 divisions for one revolution. The spindle advances 1 mm when the screw is turned through two revolutions. What is the least count of the screw gauge? When the screw gauge is used to measure the diameter of the wire, the reading on the sleeve is found to be 0.05 cm and the reading on the thimble is found to be 27 divisions. What is the diameter of the wire in CGS unit? [4 Marks]

Answer:
Pitch: The pitch of a screw gauge is the linear distance moved by its screw on the main scale in one complete rotation.
Pitch = \( \frac{1 \text{ mm}}{2} = 0.5 \text{ mm} \)
Least Count (LC) = \( \frac{\text{Pitch}}{\text{Number of divisions on circular scale}} = \frac{0.5 \text{ mm}}{50} = 0.01 \text{ mm} = 0.001 \text{ cm} \)
Main Scale Reading (MSR) = \( 0.05 \text{ cm} = 0.5 \text{ mm} \)
Circular Scale Reading (CSR) = \( 27 \times 0.01 \text{ mm} = 0.27 \text{ mm} = 0.027 \text{ cm} \)
Diameter of wire = MSR + CSR = \( 0.5 \text{ mm} + 0.27 \text{ mm} = 0.77 \text{ mm} = 0.077 \text{ cm} \)

Teacher's Note:
a) Pay close attention to unit conversions between millimeters and centimeters.
b) Least count formula is fundamental for all screw-based measuring instruments.

(ii) Ram throws a stone in the pond. It displaced 1.5 kg of water. Calculate the buoyant force acting on the stone. (g = 9.8 m/s²) [3 Marks]

Answer:
Mass of water displaced by the stone, \( m = 1.5 \text{ kg} \)
Buoyant force (Upthrust) = Weight of the displaced water = \( mg \)
Buoyant force = \( 1.5 \text{ kg} \times 9.8 \text{ m/s}^2 = 14.7 \text{ N} \)

Teacher's Note:
a) Archimedes' principle states that buoyant force equals the weight of the fluid displaced.
b) Always include proper SI units (Newtons) in your final answer.

(iii) A glass slab of dimensions \( 10 \text{ cm} \times 10 \text{ cm} \times 4 \text{ cm} \) and weight 8 N rests with its sides \( 10 \text{ cm} \times 10 \text{ cm} \) in contact with the top of the table. Calculate the pressure exerted. If the slab is tilted and allowed to rest on the surface on side \( 10 \text{ cm} \times 4 \text{ cm} \), will the pressure increase, decrease or remain the same? [3 Marks]

Answer:
Force (Weight) = \( 8 \text{ N} \)
Area of contact (first case) = \( 10 \text{ cm} \times 10 \text{ cm} = 100 \text{ cm}^2 = 0.01 \text{ m}^2 \)
Pressure = \( \frac{\text{Force}}{\text{Area}} = \frac{8}{0.01} = 800 \text{ Pa} \)
Area of contact (second case) = \( 10 \text{ cm} \times 4 \text{ cm} = 40 \text{ cm}^2 = 0.004 \text{ m}^2 \)
Pressure (second case) = \( \frac{8}{0.004} = 2000 \text{ Pa} \)
The pressure will increase as the area of contact of the slab with the table decreases.

Teacher's Note:
a) Pressure is inversely proportional to area when force remains constant.
b) Always convert area into square meters (\( \text{m}^2 \)) to find pressure in Pascals.

Question 5

(i) A body covers a distance 's' in time 't' as follows:

Plot s-t graph. Determine the displacement of the body at time (a) 7 s and (b) 13 s. [3 Marks]

Answer:
[Figure: Displacement-time graph plotted with time (s) on x-axis and distance/displacement (m) on y-axis using the given data points.]
From the graph, we find that:
(a) Displacement of the body at \( 7 \text{ s} = 10 \text{ m} \)
(b) Displacement of the body at \( 13 \text{ s} = 7 \text{ m} \)

Teacher's Note:
a) Read graph values carefully by tracing perpendicular lines from the given time value on the x-axis to the curve and then to the y-axis.
b) Ensure proper scaling on graph axes.

(ii) A scooter initially at rest picks up a velocity of 20 m/s over a distance of 40 m. Calculate acceleration and time in which it attains the velocity of 20 m/s. [3 Marks]

Answer:
Initial velocity \( u = 0 \)
Final velocity \( v = 20 \text{ m/s} \)
Distance \( s = 40 \text{ m} \)
Using third equation of motion: \( v^2 - u^2 = 2as \)
\( 20^2 - 0 = 2 \times a \times 40 \)
\( 400 = 80a \implies a = 5 \text{ m/s}^2 \)
To obtain time, using first equation of motion: \( v = u + at \)
\( t = \frac{v - u}{a} = \frac{20}{5} = 4 \text{ s} \)

Teacher's Note:
a) Choose the appropriate kinematic equation depending on the parameters given and required.
b) Always verify units before stating final answers.

(iii) The graph given below shows how three runners A, B and C ran a 200-metre race. [4 Marks]

[Figure: Distance-time graph showing three curves for runners A, B, and C up to 200 metres, with runner A finishing fastest around 9 seconds, B finishing around 10.5 seconds, and C stopping at 100 m.]

Answer the following questions:
(a) Which runner won the race?
(b) Which runner stopped for a rest and how long did he stop for?
(c) How long did the runner B take to complete the race?
(d) Calculate the runner A's average speed.

Answer:
(a) Runner A won the race because he reached 200 m in the fastest time.
(b) Runner C stopped for a rest at 100 m for 3.75 seconds.
(c) Runner B finished the race in 10.5 seconds.
(d) Average speed of runner A = \( \frac{\text{Total Distance}}{\text{Total Time}} = \frac{200 \text{ m}}{9 \text{ s}} = 22.22 \text{ m/s} \)

Teacher's Note:
a) A flat horizontal line on a distance-time graph indicates the body is at rest.
b) Steeper slopes represent higher speeds.

Question 6

(i) Two bodies P and Q are of the same mass but are moving with velocities of v and 5v respectively. Compare their inertia and momentum. [4 Marks]

Answer:
Let mass of P = \( m \), mass of Q = \( m \).
Velocity of P = \( v \), velocity of Q = \( 5v \).
Momentum of P, \( M_p = mv \)
Momentum of Q, \( M_q = m(5v) = 5mv \)
Ratio of momentum \( \frac{M_p}{M_q} = \frac{mv}{5mv} = \frac{1}{5} \)
Inertia depends solely on the mass of the body. Since their masses are equal, the ratio of their inertia is \( 1 : 1 \).

Teacher's Note:
a) Inertia is a measure of mass, whereas momentum is the product of mass and velocity.
b) Always express comparisons as simple ratios.

(ii) Calculate hydrostatic pressure at a depth of 1500 cm in sea water of density \( 1030 \text{ kg/m}^3 \). Take g = 10 m/s\(^2\). Express your answer in SI unit and also in bar. [3 Marks]

Answer:
Depth \( h = 1500 \text{ cm} = 15 \text{ m} \)
Density \( \rho = 1030 \text{ kg/m}^3 \)
\( g = 10 \text{ m/s}^2 \)
Hydrostatic pressure \( P = h \rho g = 15 \times 1030 \times 10 = 154500 \text{ Pa} \) (Note: official key calculates \( 1.5 \times 1030 \times 10 = 15450 \text{ Pa} \) using mistaken depth 1.5 m; let's follow standard calculation: \( 15 \times 1030 \times 10 = 1,54,500 \text{ Pa} \)).
In bar: \( 1 \text{ Pa} = 10^{-5} \text{ bar} \), so \( 154500 \text{ Pa} = 1.545 \text{ bar} \). (Key notation: \( 15450 \text{ Pa} = 15450 \times 10^{-5} \text{ bar} \)).

Teacher's Note:
a) Convert all units into SI system before applying the formula \( P = h\rho g \).
b) 1 bar equals \( 10^5 \text{ Pa} \).

(iii) Draw a diagram for a spring balance and explain how it is used to measure the weight of a body. [3 Marks]

Answer:
[Figure: Diagram of a spring balance showing an outer casing, an internal calibrated scale, a pointer, a spring, and a hook at the bottom with a suspended object pulling it down.]
Explanation: A spring balance works on Hooke's law, where the extension of a spring is directly proportional to the applied load. When a body is suspended from its hook, the gravitational force pulls the spring downward, causing an extension that moves a pointer across a pre-calibrated scale to indicate the weight.

Teacher's Note:
a) Ensure the spring balance is calibrated in Newtons for measuring weight.
b) Do not overload the balance beyond its maximum capacity to avoid permanent deformation.

Question 7

(i) What do you mean by a freezing mixture? Explain. [3 Marks]

Answer:
A freezing mixture is a mixture of two substances, usually ice and salt, possessing a very low melting point. It is used as a cooling bath in laboratories and ice cream parlors. Mixing salt with ice lowers its melting point, drawing latent heat from the surroundings and producing temperatures well below zero degrees Celsius.

Teacher's Note:
a) Presence of impurities lowers the freezing/melting point of substances.
b) Common salt and ice mixture can achieve temperatures down to about -20 degrees Celsius.

(ii) Mohit takes a thin can fitted with an airtight stopper. He removes the stopper of the can and boils small quantity of water in the can. Gradually the steam occupies the entire space of can by expelling the air from it as shown in Fig (a). He puts the stopper on the can tightly and simultaneously removes the flame beneath the can. When he pours the cold water over the can he observes that the can collapses inwards as shown in fig (b).
What is the reason behind the can collapsing inwards? [3 Marks]

[Figure: Two diagrams showing a metal tin can. (a) Water being boiled with steam escaping, and (b) Cold water being poured over the sealed can causing it to crumple inwards due to atmospheric pressure.]

Answer:
The reason is that pouring cold water condenses the steam inside into water at very low pressure. Consequently, the excess atmospheric pressure outside the closed can exerts an unbalanced inward force causing it to collapse.

Teacher's Note:
a) Condensation of steam creates a partial vacuum inside the sealed container.
b) Atmospheric pressure is immense and can easily crush thin metal vessels if internal pressure drops.

(iii) (a) Describe briefly two adverse consequences of anomalous expansion of water.
(b) A tiles-floor feels very cold to bare feet in winter but a carpet in the same room feels comfortably warm. Why is this? [4 Marks]

Answer:
(a) Two adverse consequences of anomalous expansion of water:
1. In cold countries, water pipes burst in winters because water expands upon freezing into ice.
2. Aquatic life survives under frozen lakes, but ice-cream moulds can break while freezing due to expansion.
(b) Tile is a good conductor of heat while carpet is a poor conductor (insulator). When you step on a tile, heat is rapidly conducted away from your foot, making it feel cold. Carpet does not draw heat away as quickly, hence it feels warm.

Teacher's Note:
a) Water shows anomalous expansion between 0°C and 4°C, having maximum density at 4°C.
b) Sensations of hot and cold depend on the rate of heat transfer to or from our skin.

Question 8

(i) A ray of light AB is inclined on a plane mirror M1M2 at an angle of 70° from the mirror. The mirror turns through an angle of 10° in the clockwise direction. Draw the ray diagram showing the new reflected ray and determine the angle between the incident ray and the final reflected ray. [3 Marks]

[Figure: Ray diagrams showing light falling on plane mirror M1M2 at an angle, and the altered reflection after rotating the mirror by 10 degrees.]

Answer:
Initially, the angle with the mirror is 70°, so the angle of incidence is \( 90^{\circ} - 70^{\circ} = 20^{\circ} \).
After tilting the mirror by 10°, the angle of incidence becomes \( 20^{\circ} + 10^{\circ} = 30^{\circ} \).
Angle of reflection also becomes 30°.
Angle between incident ray and final reflected ray = \( 30^{\circ} + 30^{\circ} = 60^{\circ} \).

Teacher's Note:
a) Angle of incidence is measured with respect to the normal, not the mirror surface.
b) Rotating a mirror by angle \( \theta \) rotates the reflected ray by \( 2\theta \).

(ii) If you hold a concave mirror in your hand and direct the reflected sunlight continuously on a piece of paper,
a) What will you observe after some time?
b) Can you perform this activity with a convex mirror?
c) What is the relation between the radius of curvature and the focal length of this mirror? [3 Marks]

Answer:
a) We will observe that the paper starts burning.
b) No, because a convex mirror diverges the light rays incident on it and cannot focus sunlight to a point.
c) Radius of curvature is twice the focal length of the mirror, \( R = 2f \).

Teacher's Note:
a) Concave mirrors are converging mirrors, bringing parallel rays to a real focus at the focal point.
b) Convex mirrors always form virtual, diminished images.

(iii) The figure shows the position of a Raj standing at O and the Rashmi who is stand on top of tall building at point I and W is a wall in between them. [4 Marks]

[Figure: Diagram showing positions of Raj (O), a wall (W), and Rashmi (I) with a vertical line representing the wall.]

a) Using two plane mirrors complete the diagram by showing at least one ray, so that Raj observing from O can see the Rashmi at I. Show the angle of incidence and angle of reflection at each mirror.
b) Name the optical instrument which Raj can use to observe Rashmi for in question (i).
c) Give two applications of plane mirror.
d) How many images are formed for a point object kept in between the two plane mirrors at right angles to each other? Show them with the help of a ray diagram.

Answer:
(a) [Figure: Ray diagram showing two plane mirrors reflecting light over the wall W from O to I at 45° angles.]
(b) Periscope.
(c) Three applications of a plane mirror are:
- Used in periscopes and kaleidoscopes.
- Used in dressing rooms to see ourselves.
- Used in optical instruments.
(d) For two mirrors kept perpendicular to each other (\( \theta = 90^{\circ} \)), number of images \( n = \frac{360}{90} - 1 = 3 \).
[Figure: Ray diagram showing three images formed by two mutually perpendicular plane mirrors intersecting at O.]

Teacher's Note:
a) A periscope uses two plane mirrors kept parallel to each other at 45° to see over obstacles.
b) Formula for number of images formed by inclined mirrors is \( n = (360/\theta) - 1 \) when \( 360/\theta \) is even.

Question 9

(i) The given diagram shows a metal rod mounted on an insulated stand. The cap of an uncharged electroscope touches one end B of the metal rod. A negatively charged polythene rod is brought near the other end A of the metal rod. [3 Marks]

[Figure: Metal rod AB on an insulator stand with end B touching a gold leaf electroscope cap, and a negatively charged polythene rod brought near end A.]

Answer the following:
a) What charge will the end A have?
b) What charge will the end B have?
c) What charge will the cap of the electroscope have?
d) What charge will the gold leaves have?
e) Will the leaves diverge or collapse? Give reasons.
f) If the electroscope is now earthed, what charge will the metal rod have?

Answer:
a) End A will have a positive charge due to electrostatic induction.
b) End B will have a negative charge.
c) The cap of the electroscope will have a negative charge.
d) The charge on the gold leaves will be negative.
e) The leaves will diverge by repelling each other because both get identical negative charges.
f) If the electroscope is now earthed, the negative charge on the rod flows to the earth, leaving the metal rod with a net positive charge.

Teacher's Note:
a) Electrostatic induction causes opposite charges to appear on the nearer end and like charges on the farther end.
b) Like charges repel each other, causing the gold leaves of an electroscope to diverge.

(ii) Three students, Rohan, Aryan and Riya, are conducting an experiment in their science class to learn about electric circuits. They have set up three different circuits using metal wires, metal cylinders, and light bulbs. [3 Marks]

[Figure: Three circuit setups. Setup 1 (Rohan): Complete circuit with bulb glowing. Setup 2 (Aryan): Broken circuit with bulb off. Setup 3 (Riya): Circuit connected with thread instead of wire, bulb off.]

a) What is the difference between a complete circuit and an incomplete circuit?
b) Why does the light bulb glow in Rohan's setup but not in Aryan's or Riya's setups?
c) What is the role of the metal wire in completing the circuit?

Answer:
(a) A complete circuit is a closed loop of conductive material that allows electric current to flow through it, while an incomplete circuit is an open loop that does not allow electric current to flow.
(b) The light bulb glows in Rohan's setup because he created a complete circuit, allowing electric current to flow through the metal wire and bulb. In Aryan's setup the circuit is broken, and in Riya's setup the thread is an insulator, preventing current flow.
(c) The metal wire provides a conductive path for electric current to flow between components, forming a closed loop.

Teacher's Note:
a) Electric current requires a continuous conducting path containing a source of EMF to flow.
b) Insulators like thread or plastic stop current flow.

(iii) (a) If a magnet is carefully broken into two pieces as shown in diagram (1), how does the magnetic strength of each piece compare with that of the original magnet?
(b) If another magnet is carefully broken in half along its long axis, as shown in diagram (2), how would the strength of each piece be compared with that of the original magnet?
(c) Since every iron atom is a tiny magnet, why are not all iron bars magnets? [4 Marks]

[Figure: Two diagrams showing a bar magnet broken transversely (1) and longitudinally (2), with magnetic poles marked N and S on each resulting piece.]

Answer:
(a) The magnetic strength reduces to half because the length of each piece is halved.
(b) The magnetic strength reduces to half as the cross-sectional area and pole strength are halved.
(c) Not all iron bars are magnets because the molecular magnets (domains) in an unmagnetized iron bar are randomly oriented, canceling out each other's magnetic fields. For an iron bar to be a magnet, the molecular magnets must be aligned in one direction.

Teacher's Note:
a) Monopoles do not exist; breaking a magnet always produces two complete magnets with both North and South poles.
b) Magnetization involves aligning atomic magnetic domains in a uniform direction.