Physics · Sample Paper 2

General instructions

Section A · Objective

1. Question 11 mark

   An electric dipole is placed in a uniform electric field. The net force on it is

   1. A.maximum
   2. B.zero
   3. C.along the field
   4. D.opposite to the field
2. Question 21 mark

   The work done in moving a charge on an equipotential surface is

   1. A.positive
   2. B.negative
   3. C.zero
   4. D.infinite
3. Question 31 mark

   The SI unit of resistivity is

   1. A.Ω
   2. B.Ω m
   3. C.Ω/m
   4. D.S
4. Question 41 mark

   The magnetic field at the centre of a circular coil of radius R carrying current I is

   1. A.$\frac{{\mu }_{0}I}{2R}$
   2. B.$\frac{{\mu }_{0}I}{2\pi R}$
   3. C.$\frac{{\mu }_{0}I}{4R}$
   4. D.${\mu }_{0}IR$
5. Question 51 mark

   A material that is strongly attracted by a magnet is

   1. A.diamagnetic
   2. B.paramagnetic
   3. C.ferromagnetic
   4. D.non-magnetic
6. Question 61 mark

   The SI unit of self-inductance is

   1. A.weber
   2. B.henry
   3. C.tesla
   4. D.farad
7. Question 71 mark

   The power factor of a purely inductive circuit is

   1. A.1
   2. B.0
   3. C.0.5
   4. D.∞
8. Question 81 mark

   Which electromagnetic waves have the shortest wavelength?

   1. A.radio waves
   2. B.microwaves
   3. C.X-rays
   4. D.gamma rays
9. Question 91 mark

   The critical angle for glass of refractive index 1.5 is about

   1. A.$30^{\circ }$
   2. B.$42^{\circ }$
   3. C.$48^{\circ }$
   4. D.$60^{\circ }$
10. Question 101 mark

    Polarisation of light proves that light is

    1. A.longitudinal
    2. B.transverse
    3. C.made of particles
    4. D.a sound wave
11. Question 111 mark

    The energy of a photon of frequency ν is

    1. A.$h\nu$
    2. B.$h/\nu$
    3. C.$\nu /h$
    4. D.$h{\nu }^2$
12. Question 121 mark

    The radius of a nucleus is proportional to

    1. A.$A$
    2. B.$A^{1/3}$
    3. C.$A^2$
    4. D.$A^{1/2}$
13. Question 131 mark

    Assertion (A): Capacitance of a capacitor increases when a dielectric slab is inserted between the plates.

    Reason (R): The dielectric reduces the electric field between the plates, reducing the potential difference for the same charge.

    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): A moving coil galvanometer can be converted into an ammeter by connecting a low resistance in parallel.

    Reason (R): The shunt carries most of the current, protecting the galvanometer.

    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): Heavy nuclei release energy when they undergo fission.

    Reason (R): The binding energy per nucleon of the product nuclei is less than that of the heavy nucleus.

    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 resistance of a semiconductor decreases with rise in temperature.

    Reason (R): More electron-hole pairs are generated at higher temperatures.

    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

   Find the electric potential at a point 0.3 m from a point charge of $+5\mu$C. How much work is needed to bring a charge of $+2\mu$C from infinity to this point?

2. Question 182 marks

   Three resistors of 2 Ω, 3 Ω and 6 Ω are connected in parallel. Find the equivalent resistance.

3. Question 192 marks

   State two properties of magnetic field lines.

4. OR

   Question 192 marks

   Name the electromagnetic waves used (i) in remote controls (ii) to kill germs in water purifiers. Give their frequency range order.

5. Question 202 marks

   An object is placed 30 cm in front of a concave mirror of focal length 15 cm. Find the position and nature of the image.

6. Question 212 marks

   State Bohr's quantisation condition. What is the radius of the second orbit of hydrogen if the first is 0.53 Å?

Section C · Short answer

1. Question 223 marks

   Derive an expression for the electric field at a point on the axis of an electric dipole.

2. Question 233 marks

   A potentiometer wire of length 4 m has a resistance of 8 Ω and is connected to a 2 V cell with negligible internal resistance. Find the potential gradient. A cell balances at 2.5 m; find its emf.

3. Question 243 marks

   Using Ampere's circuital law, derive the magnetic field inside a long straight solenoid.

4. Question 253 marks

   State Faraday's laws of electromagnetic induction. A coil of 100 turns and area $0.01{\text{m}}^2$ is in a field that changes from 0.2 T to 0.6 T in 0.1 s. Find the induced emf.

5. OR

   Question 253 marks

   Explain the working of a step-up transformer. A transformer has 100 primary and 2000 secondary turns. If the input is 220 V AC, find the output voltage. Give one source of energy loss.

6. Question 263 marks

   In Young's double-slit experiment, the slits are 0.2 mm apart and the screen is 1 m away. Light of wavelength 600 nm is used. Find the fringe width and the distance of the third bright fringe from the centre.

7. Question 273 marks

   Write Einstein's photoelectric equation. Light of wavelength 400 nm falls on a metal of work function 2.0 eV. Find the maximum kinetic energy of the emitted electrons.

8. Question 283 marks

   Calculate the binding energy of a helium nucleus (${}_2^{4}He$). Mass of proton = 1.00728 u, neutron = 1.00867 u, He nucleus = 4.00151 u. (1 u = 931.5 MeV)

Section D · Case-based

1. Question 294 marks

   Case study — Solar-powered street lights. A village installs street lights powered by solar cells. During the day, each solar panel charges a battery; at night, the battery powers LED lamps. A solar cell is a p-n junction that produces an emf when light falls on it. LEDs are p-n junctions that emit light when forward biased.

   (i) On which principle does a solar cell work? (1 mark)

   (ii) Why are LEDs preferred over incandescent bulbs? Give one reason. (1 mark)

   (iii) Explain the three basic processes involved in the working of a solar cell. (2 marks)

   OR

   (iii) Why should the band gap of the semiconductor used in an LED for visible light be about 1.8–3 eV? (2 marks)

2. Question 304 marks

   Case study — The astronomical telescope. An amateur astronomer uses a refracting telescope with an objective of focal length 100 cm and an eyepiece of focal length 5 cm to look at the Moon. In normal adjustment, the final image is formed at infinity.

   (i) Find the magnifying power in normal adjustment. (1 mark)

   (ii) What is the length of the telescope in normal adjustment? (1 mark)

   (iii) Why should the objective of a telescope have a large aperture? Give two reasons. (2 marks)

   OR

   (iii) Why are large modern telescopes reflecting rather than refracting? Give two reasons. (2 marks)

Section E · Long answer

1. Question 315 marks

   Derive the relation between drift velocity and current in a conductor. Hence deduce Ohm's law and show that resistivity $\rho =\frac{m}{n{e}^2\tau }$.

2. OR

   Question 315 marks

   Derive the expressions for the equivalent emf and internal resistance of two cells connected in parallel. Two cells of emf 2 V and 1.5 V with internal resistances 1 Ω and 0.5 Ω are connected in parallel. Find the equivalent emf.

3. Question 325 marks

   Derive the expression for the force between two long parallel current-carrying conductors. Hence define one ampere. Find the force per metre between two wires 10 cm apart carrying 5 A each.

4. OR

   Question 325 marks

   Explain the principle and working of a moving coil galvanometer. How is its current sensitivity increased? How can it be converted into a voltmeter?

5. Question 335 marks

   Describe diffraction of light at a single slit. Derive the condition for the first minimum and find the angular width of the central maximum. Light of wavelength 500 nm falls on a slit of width 0.1 mm; find the angular width of the central maximum.

6. OR

   Question 335 marks

   Derive the relation $\frac{{\mu }_2}{v}-\frac{{\mu }_1}{u}=\frac{{\mu }_2-{\mu }_1}{R}$ for refraction at a convex spherical surface. A glass sphere ($\mu =1.5$) of radius 10 cm has an object in air 30 cm from its surface; find the position of the image formed by the first surface.