Physics · Sample Paper 3

General instructions

Section A · Objective

1. Question 11 mark

   Which of these is a dimensionless quantity?

   1. A.strain
   2. B.stress
   3. C.force
   4. D.pressure
2. Question 21 mark

   1 light year is a unit of

   1. A.time
   2. B.distance
   3. C.speed
   4. D.intensity
3. Question 31 mark

   The slope of a position–time graph gives

   1. A.acceleration
   2. B.velocity
   3. C.displacement
   4. D.force
4. Question 41 mark

   A ball is thrown horizontally from a height. Ignoring air resistance, its horizontal velocity

   1. A.increases
   2. B.decreases
   3. C.stays constant
   4. D.becomes zero
5. Question 51 mark

   The SI unit of impulse is

   1. A.N
   2. B.N s
   3. C.N/s
   4. D.kg m/s²
6. Question 61 mark

   Work done by a force F = (2î + 3ĵ) N in displacing a body by (3î + 2ĵ) m is

   1. A.6 J
   2. B.12 J
   3. C.13 J
   4. D.5 J
7. Question 71 mark

   The centre of mass of a uniform semicircular ring of radius R lies at a distance from the centre of

   1. A.$R/2$
   2. B.$2R/\pi$
   3. C.$4R/3\pi$
   4. D.0
8. Question 81 mark

   Kepler's third law states that $T^2$ is proportional to

   1. A.r
   2. B.$r^2$
   3. C.$r^3$
   4. D.$1/r$
9. Question 91 mark

   Within the elastic limit, stress is proportional to strain. This is

   1. A.Pascal's law
   2. B.Hooke's law
   3. C.Newton's law
   4. D.Bernoulli's principle
10. Question 101 mark

    The viscous force on a small sphere moving through a fluid at low speed is given by

    1. A.Bernoulli's equation
    2. B.Stokes' law
    3. C.Pascal's law
    4. D.Archimedes' principle
11. Question 111 mark

    The SI unit of specific heat capacity is

    1. A.J kg${}^{-1}$ K${}^{-1}$
    2. B.J K⁻¹
    3. C.J kg⁻¹
    4. D.W m⁻¹ K⁻¹
12. Question 121 mark

    The mean free path of gas molecules increases when

    1. A.pressure increases
    2. B.density decreases
    3. C.temperature falls at constant pressure
    4. D.molecular size increases
13. Question 131 mark

    Assertion (A): In uniform circular motion, the speed is constant but the velocity changes.

    Reason (R): The direction of velocity changes continuously.

    1. A.Both Assertion (A) and Reason (R) are true, and R is the correct explanation of A.
    2. B.Both Assertion (A) and Reason (R) are true, but R is not the correct explanation of A.
    3. C.Assertion (A) is true, but Reason (R) is false.
    4. D.Assertion (A) is false, but Reason (R) is true.
14. Question 141 mark

    Assertion (A): It is easier to pull a lawn roller than to push it.

    Reason (R): Pulling at an angle reduces the normal reaction and hence friction.

    1. A.Both Assertion (A) and Reason (R) are true, and R is the correct explanation of A.
    2. B.Both Assertion (A) and Reason (R) are true, but R is not the correct explanation of A.
    3. C.Assertion (A) is true, but Reason (R) is false.
    4. D.Assertion (A) is false, but Reason (R) is true.
15. Question 151 mark

    Assertion (A): The time period of a simple pendulum does not depend on the mass of the bob.

    Reason (R): $T=2\pi \sqrt{l/g}$.

    1. A.Both Assertion (A) and Reason (R) are true, and R is the correct explanation of A.
    2. B.Both Assertion (A) and Reason (R) are true, but R is not the correct explanation of A.
    3. C.Assertion (A) is true, but Reason (R) is false.
    4. D.Assertion (A) is false, but Reason (R) is true.
16. Question 161 mark

    Assertion (A): The efficiency of a Carnot engine can be 100%.

    Reason (R): A Carnot engine is a reversible engine.

    1. A.Both Assertion (A) and Reason (R) are true, and R is the correct explanation of A.
    2. B.Both Assertion (A) and Reason (R) are true, but R is not the correct explanation of A.
    3. C.Assertion (A) is true, but Reason (R) is false.
    4. D.Assertion (A) is false, but Reason (R) is true.

Section B · Very short answer

1. Question 172 marks

   The length of a rod measured in three trials is 2.63 cm, 2.56 cm and 2.42 cm. Find the mean value and the mean absolute error.

2. Question 182 marks

   Draw (describe) the position–time graph of a body at rest and of a body moving with uniform velocity.

3. Question 192 marks

   Why is the weight of a body at the poles more than at the equator? Give two reasons.

4. Question 202 marks

   State Pascal's law and give one application.

5. OR

   Question 202 marks

   Why do small raindrops fall with a smaller terminal velocity than large drops?

6. Question 212 marks

   Distinguish between transverse and longitudinal waves with one example each.

Section C · Short answer

1. Question 223 marks

   Show that for a projectile, the horizontal range is maximum at $45^{\circ }$. Find the maximum range for a speed of $20{\text{m s}}^{-1}$.

2. Question 233 marks

   A 5 kg block on a horizontal surface is pulled by a 30 N force. If the coefficient of kinetic friction is 0.4, find the acceleration and the distance covered in 4 s starting from rest.

3. Question 243 marks

   Define power. A car of mass 1000 kg moves up a slope rising 1 m for every 20 m along the road at $10{\text{m s}}^{-1}$. Ignoring friction, find the power needed.

4. Question 253 marks

   Define torque and angular momentum. Show that torque equals the rate of change of angular momentum.

5. Question 263 marks

   How much heat is needed to convert 1 kg of ice at −10 °C into water at 20 °C? ($c_{ice}=2100$, $c_{water}=4200{\text{J kg}}^{-1}{\text{K}}^{-1}$, $L_f=3.36\times 10^5{\text{J kg}}^{-1}$)

6. Question 273 marks

   Show that the motion of a mass on a horizontal spring is simple harmonic and find its time period.

7. OR

   Question 273 marks

   What are beats? Two tuning forks give 4 beats per second. One has a frequency of 256 Hz; when the other is loaded with wax, the beats decrease. Find its frequency.

8. Question 283 marks

   Derive the relation between pressure and the mean kinetic energy of the molecules of an ideal gas.

Section D · Case-based

1. Question 294 marks

   Case study — Roller coaster. A roller-coaster car of mass 500 kg starts from rest at the top of a 45 m high hill and rolls down to the bottom. Ignore friction.

   (i) What is its potential energy at the top (take the bottom as zero)? (1 mark)

   (ii) What is its speed at the bottom? (1 mark)

   (iii) It next climbs a hill of height 25 m. Find its speed at the top of that hill. (2 marks)

   OR

   (iii) If 20% of the energy is lost to friction on the way down, find its speed at the bottom. (2 marks)

2. Question 304 marks

   Case study — Car engine. A petrol engine takes in heat from burning fuel, converts part of it into work and rejects the rest to the surroundings. In one cycle it takes in 2000 J and rejects 1400 J.

   (i) Find the work done per cycle. (1 mark)

   (ii) Find the efficiency of the engine. (1 mark)

   (iii) State the second law of thermodynamics (Kelvin–Planck) and explain why the engine must reject heat. (2 marks)

   OR

   (iii) If the engine works between 600 K and 300 K, what is the maximum (Carnot) efficiency? Compare it with the actual efficiency. (2 marks)

Section E · Long answer

1. Question 315 marks

   Derive the three equations of motion for uniformly accelerated motion by calculus. A car accelerates from $10{\text{m s}}^{-1}$ to $30{\text{m s}}^{-1}$ in 5 s. Find its acceleration and the distance covered.

2. Question 325 marks

   Derive an expression for the gravitational potential energy of a body of mass m at a distance r from the centre of the Earth. Hence derive the escape speed and calculate it for the Earth. ($g=9.8{\text{m s}}^{-2}$, $R=6.4\times 10^6$ m)

3. OR

   Question 325 marks

   State and prove Bernoulli's theorem for the streamline flow of an ideal fluid. Give two applications.

4. Question 335 marks

   Explain the formation of stationary waves in an open organ pipe. Show that all harmonics are present. An open pipe is 0.5 m long; find the frequencies of the first two harmonics. (Speed of sound 340 m/s)