Physics · Sample Paper 1

General instructions

Section A · Multiple choice

1. Question 14 marks

   If force F, length L and time T are taken as base quantities, the dimensions of mass are

   1. A.$[FL^{-1}T^2]$
   2. B.$[FLT^{-2}]$
   3. C.$[FL^{-1}T^{-1}]$
   4. D.$[FL^2T^{-2}]$
2. Question 24 marks

   A particle starts from rest with acceleration $a = 2t$ (SI). Its displacement in the first 3 s is

   1. A.9 m
   2. B.18 m
   3. C.6 m
   4. D.27 m
3. Question 34 marks

   Two projectiles are thrown with the same speed at angles $\theta$ and $90^\circ - \theta$. The ratio of their maximum heights is

   1. A.$\tan\theta$
   2. B.$\tan^2\theta$
   3. C.$\cot\theta$
   4. D.1
4. Question 44 marks

   Masses 3 kg and 2 kg hang from the two ends of a light string over a frictionless pulley. The acceleration of the system is

   1. A.$1\ \text{m s}^{-2}$
   2. B.$2\ \text{m s}^{-2}$
   3. C.$5\ \text{m s}^{-2}$
   4. D.$4\ \text{m s}^{-2}$
5. Question 54 marks

   A force $F = (3x^2)$ N acts on a particle moving along x. The work done from $x = 0$ to $x = 2$ m is

   1. A.4 J
   2. B.8 J
   3. C.12 J
   4. D.6 J
6. Question 64 marks

   A disc rolls without slipping down an incline of angle $\theta$. Its acceleration is

   1. A.$g\sin\theta$
   2. B.$\tfrac23g\sin\theta$
   3. C.$\tfrac12g\sin\theta$
   4. D.$\tfrac57g\sin\theta$
7. Question 74 marks

   A satellite orbits at height R above the Earth's surface (R = Earth's radius). Its orbital speed compared with a satellite close to the surface is

   1. A.$\tfrac12$
   2. B.$\tfrac{1}{\sqrt2}$
   3. C.$\sqrt2$
   4. D.2
8. Question 84 marks

   A sphere falls through a viscous liquid with terminal velocity v. A sphere of the same material with twice the radius reaches

   1. A.2v
   2. B.4v
   3. C.v/2
   4. D.$\sqrt2 v$
9. Question 94 marks

   One mole of an ideal monatomic gas is heated at constant pressure through 10 K. The heat absorbed is ($R = 8.3$ J mol⁻¹ K⁻¹)

   1. A.124.5 J
   2. B.207.5 J
   3. C.83 J
   4. D.166 J
10. Question 104 marks

    A particle in SHM has amplitude A. At what displacement is its kinetic energy equal to its potential energy?

    1. A.$A/2$
    2. B.$A/\sqrt2$
    3. C.$A/4$
    4. D.$\sqrt3A/2$
11. Question 114 marks

    Two sources of 256 Hz and 260 Hz are sounded together. The time between successive maxima of loudness is

    1. A.0.25 s
    2. B.4 s
    3. C.0.5 s
    4. D.2 s
12. Question 124 marks

    An electric dipole of moment p is placed at $60^\circ$ to a uniform field E. The work needed to turn it to $180^\circ$ is

    1. A.$\tfrac32pE$
    2. B.$pE$
    3. C.$\tfrac12pE$
    4. D.$2pE$
13. Question 134 marks

    Two capacitors 2 μF and 4 μF are in parallel across 10 V. The total energy stored is

    1. A.300 μJ
    2. B.150 μJ
    3. C.600 μJ
    4. D.60 μJ
14. Question 144 marks

    In a potentiometer, the balancing length for a cell of emf 1.5 V is 60 cm. For another cell it is 80 cm. The emf of the second cell is

    1. A.1.125 V
    2. B.2 V
    3. C.1.8 V
    4. D.2.5 V
15. Question 154 marks

    Two long parallel wires 10 cm apart carry 5 A each in the same direction. The force per metre between them is

    1. A.$5\times10^{-5}$ N, attractive
    2. B.$5\times10^{-5}$ N, repulsive
    3. C.$10^{-4}$ N, attractive
    4. D.$2.5\times10^{-5}$ N, attractive
16. Question 164 marks

    A coil of self-inductance 0.5 H carries a current changing at 4 A/s. The induced emf is

    1. A.2 V
    2. B.8 V
    3. C.0.125 V
    4. D.4.5 V
17. Question 174 marks

    A convex lens (f = 20 cm) and a concave lens (f = 30 cm) are placed in contact. The combination is

    1. A.converging, f = 60 cm
    2. B.diverging, f = 60 cm
    3. C.converging, f = 12 cm
    4. D.diverging, f = 12 cm
18. Question 184 marks

    In a single-slit diffraction pattern, if the slit width is halved, the width of the central maximum

    1. A.halves
    2. B.doubles
    3. C.stays the same
    4. D.becomes four times
19. Question 194 marks

    The de Broglie wavelength of an electron and a photon are equal. The ratio of the photon's energy to the electron's kinetic energy is (v ≪ c)

    1. A.2c/v
    2. B.c/2v
    3. C.c/v
    4. D.v/c
20. Question 204 marks

    The output of a two-input NAND gate is 0 only when

    1. A.both inputs are 0
    2. B.both inputs are 1
    3. C.one input is 1
    4. D.inputs differ

Section B · Numerical value

1. Question 214 marks

   The rms speed of oxygen molecules at a certain temperature is $400\ \text{m s}^{-1}$. Find the rms speed (in m s⁻¹) of hydrogen molecules at the same temperature.

2. Question 224 marks

   A series LC circuit has L = 1 mH and C = 10 μF. Find its resonant angular frequency in rad/s.

3. Question 234 marks

   Find the number of spectral lines emitted when electrons in a sample of hydrogen atoms fall from n = 5 to the ground state.

4. Question 244 marks

   A radioactive sample decays to 1/16 of its initial activity in 40 days. Find its half-life in days.

5. Question 254 marks

   A wire 2 m long with cross-section 1 mm² stretches by 1 mm under a load of 100 N. Find Young's modulus in units of $10^{10}$ N m⁻².