Physics · Sample Paper 3

General instructions

Section A · Multiple choice

1. Question 14 marks

   The dimensions of $\frac{1}{2}{\epsilon }_0{E}^2$ (E = electric field) are those of

   1. A.energy
   2. B.energy density (pressure)
   3. C.force
   4. D.power
2. Question 24 marks

   A particle's position is $x=t^3-6t^2+9t$ (SI). It comes to rest momentarily at

   1. A.t = 1 s and 3 s
   2. B.t = 2 s only
   3. C.t = 0 only
   4. D.t = 3 s only
3. Question 34 marks

   A stone is projected at $60^{\circ }$ with speed $20{\text{m s}}^{-1}$. Its speed at the highest point is

   1. A.$10{\text{m s}}^{-1}$
   2. B.$20{\text{m s}}^{-1}$
   3. C.$10\sqrt{3}{\text{m s}}^{-1}$
   4. D.0
4. Question 44 marks

   A block of mass m is placed on a smooth incline of angle θ in a lift accelerating upward at a. The normal reaction is

   1. A.$m(g+a)\cos \theta$
   2. B.$mg\cos \theta$
   3. C.$m(g-a)\cos \theta$
   4. D.$m(g+a)$
5. Question 54 marks

   A body of mass 2 kg moving at $3{\text{m s}}^{-1}$ collides elastically head-on with a 1 kg body at rest. The velocity of the 1 kg body after collision is

   1. A.$4{\text{m s}}^{-1}$
   2. B.$2{\text{m s}}^{-1}$
   3. C.$3{\text{m s}}^{-1}$
   4. D.$6{\text{m s}}^{-1}$
6. Question 64 marks

   A thin rod of length L and mass M is pivoted at one end and released from horizontal. Its angular speed when vertical is

   1. A.$\sqrt{\frac{3g}{L}}$
   2. B.$\sqrt{\frac{g}{L}}$
   3. C.$\sqrt{\frac{6g}{L}}$
   4. D.$\sqrt{\frac{2g}{L}}$
7. Question 74 marks

   Two satellites orbit the Earth at radii r and 4r. The ratio of their periods $T_1:T_2$ is

   1. A.1 : 8
   2. B.1 : 4
   3. C.1 : 2
   4. D.1 : 16
8. Question 84 marks

   A soap bubble of radius r is blown. The work done against surface tension S is

   1. A.$4\pi r^{2}S$
   2. B.$8\pi r^{2}S$
   3. C.$2\pi r^{2}S$
   4. D.$16\pi r^{2}S$
9. Question 94 marks

   Two rods of equal length and area with conductivities K and 2K are joined in series. The equivalent conductivity is

   1. A.$\frac{4K}{3}$
   2. B.$\frac{3K}{2}$
   3. C.3K
   4. D.$\frac{2K}{3}$
10. Question 104 marks

    The total energy of a particle in SHM with amplitude A is E. At displacement A/2, its kinetic energy is

    1. A.$\frac{E}{4}$
    2. B.$\frac{3E}{4}$
    3. C.$\frac{E}{2}$
    4. D.E
11. Question 114 marks

    The speed of a transverse wave on a string is doubled when the tension is

    1. A.doubled
    2. B.made four times
    3. C.halved
    4. D.made eight times
12. Question 124 marks

    A charge q is placed at the centre of the line joining two equal charges Q. The system is in equilibrium if q equals

    1. A.$-Q/4$
    2. B.$-Q/2$
    3. C.$Q/4$
    4. D.$-Q$
13. Question 134 marks

    A parallel-plate capacitor (capacitance C) is half filled with a dielectric slab of constant K, parallel to the plates and of half the gap thickness. The new capacitance is

    1. A.$\frac{2KC}{K+1}$
    2. B.$\frac{(K+1)C}{2}$
    3. C.KC
    4. D.$\frac{KC}{2}$
14. Question 144 marks

    In a meter bridge, the balance point is at 40 cm with R = 6 Ω in the left gap. The unknown resistance in the right gap is

    1. A.4 Ω
    2. B.9 Ω
    3. C.6 Ω
    4. D.12 Ω
15. Question 154 marks

    An electron moving perpendicular to a uniform magnetic field completes a circle in time T. If its speed is doubled, the time becomes

    1. A.T/2
    2. B.T
    3. C.2T
    4. D.4T
16. Question 164 marks

    A conducting loop is pulled out of a magnetic field at constant speed. The force needed is proportional to

    1. A.v
    2. B.$v^2$
    3. C.$1/v$
    4. D.independent of v
17. Question 174 marks

    The average power consumed in a series LCR circuit is

    1. A.$V_{rms}{I}_{rms}$
    2. B.$V_{rms}{I}_{rms}\cos \varphi$
    3. C.$V_0{I}_0$
    4. D.zero
18. Question 184 marks

    A convex lens of focal length 20 cm (μ = 1.5) is immersed in water (μ = 4/3). Its new focal length is

    1. A.40 cm
    2. B.80 cm
    3. C.20 cm
    4. D.60 cm
19. Question 194 marks

    In YDSE, the intensity at the central maximum is $I_0$. At a point where the path difference is $\lambda /4$, the intensity is

    1. A.$I_0/2$
    2. B.$I_0/4$
    3. C.$3I_0/4$
    4. D.0
20. Question 204 marks

    The output of a two-input NOR gate is 1 only when

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

Section B · Numerical value

1. Question 214 marks

   A 4 kg block is pulled along a rough floor ($\mu =0.5$) by a horizontal force of 32 N. Find its acceleration in m s⁻² (g = 10).

2. Question 224 marks

   Find the energy (in mJ) stored in a 20 μF capacitor charged to 100 V.

3. Question 234 marks

   Light of energy 5 eV falls on a metal of work function 3 eV. Find the stopping potential in volts.

4. Question 244 marks

   A simple pendulum has a period of 2 s on Earth. Find its period (in s) on a planet where g is one-fourth of Earth's.

5. Question 254 marks

   Two long parallel wires 1 m apart carry 10 A each. Find the force per metre between them in units of $10^{-6}$ N/m.