Physics · Sample Paper 1

General instructions

Section A · Objective

1. Question 11 mark

   The SI unit of electric flux is

   1. A.N C$^{-1}$
   2. B.N m$^2$ C$^{-1}$
   3. C.C m$^{-2}$
   4. D.V m
2. Question 21 mark

   Two capacitors of 4 μF and 12 μF are joined in series. The equivalent capacitance is

   1. A.16 μF
   2. B.3 μF
   3. C.8 μF
   4. D.48 μF
3. Question 31 mark

   A wire is stretched to double its length. Its resistance becomes

   1. A.double
   2. B.half
   3. C.four times
   4. D.same
4. Question 41 mark

   A charged particle moves parallel to a uniform magnetic field. The force on it is

   1. A.maximum
   2. B.zero
   3. C.qvB
   4. D.along the field
5. Question 51 mark

   Which material has a small negative magnetic susceptibility?

   1. A.iron
   2. B.aluminium
   3. C.copper
   4. D.nickel
6. Question 61 mark

   Lenz's law is a consequence of conservation of

   1. A.charge
   2. B.momentum
   3. C.energy
   4. D.mass
7. Question 71 mark

   At resonance in a series LCR circuit, the impedance is

   1. A.maximum
   2. B.equal to R
   3. C.zero
   4. D.$X_L + X_C$
8. Question 81 mark

   Which electromagnetic waves are used in radar?

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

   The power of a convex lens of focal length 25 cm is

   1. A.+4 D
   2. B.−4 D
   3. C.+0.25 D
   4. D.+25 D
10. Question 101 mark

    In Young's double-slit experiment, if the slit separation is doubled, the fringe width

    1. A.doubles
    2. B.halves
    3. C.stays the same
    4. D.becomes four times
11. Question 111 mark

    The stopping potential in the photoelectric effect depends on the

    1. A.intensity of light
    2. B.frequency of light
    3. C.area of the plate
    4. D.time of exposure
12. Question 121 mark

    Nuclear fusion in the Sun converts

    1. A.helium into hydrogen
    2. B.hydrogen into helium
    3. C.uranium into barium
    4. D.carbon into oxygen
13. Question 131 mark

    Assertion (A): The electric field inside a charged conducting sphere is zero.

    Reason (R): Charge on a conductor resides on its outer surface.

    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): The Lyman series lies in the ultraviolet region.

    Reason (R): Lyman lines arise from transitions ending at n = 1, which involve large energy differences.

    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): A p-n junction diode conducts in forward bias.

    Reason (R): Forward bias increases the width of the depletion layer.

    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): A diamond sparkles brilliantly.

    Reason (R): Diamond has a large critical angle, so light escapes easily.

    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

   Two point charges of $+2\ \mu$C and $+8\ \mu$C are 30 cm apart. Find the force between them.

2. Question 182 marks

   A cell of emf 2 V and internal resistance 0.5 Ω is connected to a 3.5 Ω resistor. Find the current and the terminal voltage.

3. Question 192 marks

   What is displacement current? Why did Maxwell need it?

4. Question 202 marks

   Find the de Broglie wavelength of an electron accelerated through 100 V.

5. OR

   Question 202 marks

   The work function of a metal is 2.0 eV. Find its threshold wavelength.

6. Question 212 marks

   Draw (or describe) the binding energy per nucleon curve and state two conclusions from it.

Section C · Short answer

1. Question 223 marks

   A parallel-plate capacitor of 10 μF is charged to 100 V. Find the energy stored. If a dielectric of K = 5 is inserted with the battery still connected, find the new capacitance, charge and energy.

2. Question 233 marks

   State Kirchhoff's rules. Use them to derive the balance condition of a Wheatstone bridge.

3. Question 243 marks

   A proton enters a magnetic field of 0.5 T at right angles with speed $2\times10^6\ \text{m s}^{-1}$. Find the radius of its path and its frequency of revolution. ($m_p = 1.67\times10^{-27}$ kg)

4. Question 253 marks

   A rod 0.5 m long moves at $10\ \text{m s}^{-1}$ perpendicular to a 0.4 T field. Find the emf induced. If the rod is part of a circuit of resistance 2 Ω, find the current and the force needed to keep it moving.

5. Question 263 marks

   State Huygens' principle. Use it to prove the law of refraction.

6. OR

   Question 263 marks

   Unpolarised light of intensity $I_0$ passes through two polaroids whose axes are at $60^\circ$. Find the intensity after each polaroid. State Malus' law.

7. Question 273 marks

   Find the wavelength of the first line of the Balmer series of hydrogen. ($R = 1.1\times10^7\ \text{m}^{-1}$)

8. Question 283 marks

   Explain the working of a full-wave rectifier with a circuit diagram and input/output waveforms.

Section D · Case-based

1. Question 294 marks

   Case study — Optical fibres. Optical fibres carry internet data as light. A fibre has a glass core of refractive index 1.5 surrounded by cladding of a lower index. Light entering the core keeps reflecting at the core–cladding boundary with almost no loss.

   (i) Name the phenomenon that keeps light inside the fibre. (1 mark)

   (ii) State two conditions for it. (1 mark)

   (iii) Find the critical angle for a core of index 1.5 in air. (2 marks)

   OR

   (iii) Why is the cladding given a lower refractive index than the core? Give one advantage of optical fibres over copper cables. (2 marks)

2. Question 304 marks

   Case study — Transformers on the grid. Power stations generate electricity at about 11 kV. It is stepped up to around 220 kV for long-distance transmission and stepped down before reaching homes at 220 V.

   (i) Why is power transmitted at high voltage? (1 mark)

   (ii) A transformer has 100 turns in the primary and 2000 in the secondary. If the input is 220 V, find the output voltage. (1 mark)

   (iii) Name two energy losses in a transformer and how each is reduced. (2 marks)

   OR

   (iii) Why can't a transformer work on DC? (2 marks)

Section E · Long answer

1. Question 315 marks

   Using Gauss's law, derive the electric field due to (i) an infinitely long straight charged wire and (ii) an infinite plane sheet of charge. Find the field 10 cm from a wire with $\lambda = 2\ \mu\text{C m}^{-1}$.

2. OR

   Question 315 marks

   Derive the expression for the capacitance of a parallel-plate capacitor. Show that the energy stored is $\tfrac12CV^2$ and find the energy density of the field.

3. Question 325 marks

   Derive the impedance of a series LCR circuit using a phasor diagram. A series LCR circuit has R = 30 Ω, $X_L$ = 80 Ω, $X_C$ = 40 Ω, with a 200 V supply. Find the impedance, current and power factor.

4. OR

   Question 325 marks

   Define self-inductance. Derive an expression for the self-inductance of a long solenoid. Show that the energy stored in an inductor is $\tfrac12LI^2$.

5. Question 335 marks

   Derive the lens maker's formula. A convex lens of glass ($\mu = 1.5$) has radii of curvature 20 cm and 30 cm. Find its focal length and power.

6. OR

   Question 335 marks

   Draw a ray diagram of a compound microscope with the final image at the near point and derive its magnifying power. If $f_o = 1$ cm, $f_e = 5$ cm and the tube length is 15 cm, find the approximate magnification in normal adjustment (D = 25 cm).