Physics · Sample Paper 2

General instructions

Section A · Multiple choice

1. Question 14 marks

   The quantity $\frac{1}{\sqrt{{\mu }_0{\epsilon }_0}}$ has the dimensions of

   1. A.force
   2. B.velocity
   3. C.energy
   4. D.acceleration
2. Question 24 marks

   A body starting from rest covers distances in successive equal intervals of time with uniform acceleration. The ratio of distances in the 1st, 2nd and 3rd seconds is

   1. A.1 : 2 : 3
   2. B.1 : 3 : 5
   3. C.1 : 4 : 9
   4. D.1 : 1 : 1
3. Question 34 marks

   A boat crosses a river 100 m wide at $5{\text{m s}}^{-1}$ relative to water, heading perpendicular to the bank. The river flows at $3{\text{m s}}^{-1}$. The drift downstream is

   1. A.30 m
   2. B.60 m
   3. C.80 m
   4. D.100 m
4. Question 44 marks

   A block of mass 2 kg on a rough horizontal surface ($\mu =0.25$) is pulled by a horizontal force of 10 N. Its acceleration is

   1. A.$5{\text{m s}}^{-2}$
   2. B.$2.5{\text{m s}}^{-2}$
   3. C.$1{\text{m s}}^{-2}$
   4. D.0
5. Question 54 marks

   A bob of mass m tied to a string of length l is whirled in a vertical circle. The minimum speed at the lowest point to complete the circle is

   1. A.$\sqrt{gl}$
   2. B.$\sqrt{3gl}$
   3. C.$\sqrt{5gl}$
   4. D.$\sqrt{2gl}$
6. Question 64 marks

   A ring, a disc and a solid sphere of the same mass and radius roll down the same incline from rest. Which reaches the bottom first?

   1. A.ring
   2. B.disc
   3. C.solid sphere
   4. D.all together
7. Question 74 marks

   The ratio of the kinetic energy to the total energy of a satellite in a circular orbit is

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

   A capillary tube of radius r raises water to height h. For a tube of radius 2r, the height is

   1. A.2h
   2. B.h
   3. C.h/2
   4. D.h/4
9. Question 94 marks

   An ideal gas expands adiabatically to twice its volume. If $\gamma =1.5$, the ratio of final to initial temperature is

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

    Two springs of constants k and 2k are connected in series. The effective spring constant is

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

    The fundamental frequency of an open pipe is 300 Hz. If one end is closed, the fundamental becomes

    1. A.150 Hz
    2. B.300 Hz
    3. C.600 Hz
    4. D.100 Hz
12. Question 124 marks

    The electric flux through one face of a cube with a charge q at its centre is

    1. A.$q/{\epsilon }_0$
    2. B.$q/6{\epsilon }_0$
    3. C.$q/8{\epsilon }_0$
    4. D.$q/24{\epsilon }_0$
13. Question 134 marks

    A parallel-plate capacitor is connected to a battery and a dielectric of constant K is inserted. The energy stored

    1. A.decreases K times
    2. B.increases K times
    3. C.remains the same
    4. D.increases $K^2$ times
14. Question 144 marks

    A wire is stretched uniformly so that its length doubles. Its resistance becomes

    1. A.2R
    2. B.4R
    3. C.R/2
    4. D.R/4
15. Question 154 marks

    A charged particle enters a uniform magnetic field at $60^{\circ }$ to it. Its path is a

    1. A.circle
    2. B.straight line
    3. C.helix
    4. D.parabola
16. Question 164 marks

    The mutual inductance of two coils depends on

    1. A.the current in them
    2. B.their geometry, separation and the core
    3. C.the rate of change of current
    4. D.the induced emf
17. Question 174 marks

    In a series LCR circuit, $V_L=V_C=100$ V and $V_R=50$ V. The supply voltage is

    1. A.50 V
    2. B.150 V
    3. C.250 V
    4. D.100 V
18. Question 184 marks

    A prism of angle $60^{\circ }$ gives minimum deviation $30^{\circ }$. Its refractive index is

    1. A.$\sqrt{2}$
    2. B.$\sqrt{3}$
    3. C.1.5
    4. D.$\frac{3}{2\sqrt{2}}$
19. Question 194 marks

    If the frequency of incident light is doubled (above threshold), the maximum kinetic energy of photoelectrons

    1. A.doubles
    2. B.becomes more than double
    3. C.becomes less than double
    4. D.is unchanged
20. Question 204 marks

    The wavelength of the first Lyman line compared with the first Balmer line of hydrogen is

    1. A.longer
    2. B.shorter
    3. C.equal
    4. D.cannot be compared

Section B · Numerical value

1. Question 214 marks

   The acceleration due to gravity on a planet with twice the Earth's mass and twice its radius is $x{\text{m s}}^{-2}$ (take $g_{Earth}=10$). Find x.

2. Question 224 marks

   Three resistors of 6 Ω each are connected: two in parallel, and this combination in series with the third. Find the equivalent resistance in ohms.

3. Question 234 marks

   Find the number of degrees of freedom of a rigid diatomic molecule at room temperature.

4. Question 244 marks

   An object is placed 30 cm in front of a convex lens of focal length 20 cm. Find the image distance in cm.

5. Question 254 marks

   A nucleus with mass number 216 undergoes a series of decays to mass number 200. How many α-particles are emitted?