NEST Exam 2023 Question Paper Physics Shift II

Use the following values for constants.

Acceleration due to gravity on Earth g 10.00 m·s−2
Boltzmann constant kB 1.38 × 10−23 J·K−1
Current Mass of the Sun Ms 2.00 × 1030 kg
Current Radius of the Sun Rs 7.00 × 108 m
Magnitude of the electron charge e 1.60 × 10−19 C
Mass of the electron me 9.11 × 10−31 kg
Mass of the proton mp 1.67 × 10−27 kg
Atomic Mass Unit u 931.50 MeV/c2
Permeability of free space µ0 1.26 × 10−6 H·m−1
Permittivity of free space 0 8.85 × 10−12 F·m−1
Planck’s constant h 6.63 × 10−34 J·s
Avogadro Constant NA 6.02 × 1023 mol−1
Speed of light in vacuum c 3.00 × 108 m·s−1
Stefan-Boltzmann constant σ 5.67 × 10−8 W·m−2 · K−4
Universal Gas constant R 8.31 J·K−1 · mol−1
3
Universal Gravitational constant G 6.67 × 10−11 kg−1 ·m · s−2
Wien’s constant b 2.90 × 10−3 m·K
π ≈ 3.14
ln 2 ≈ 0.69
ln 3 ≈ 1.10
ln 10 ≈ 2.30
Base of the Napierian logarithm e ≈ 2.72

SET B
ˆ The first 12 questions are multiple choice questions with only one answer correct.
The candidate gets 2.5 marks for a correct answer and −1 for an incorrect answer.

ˆ Questions 13 − 17 are multiple choice questions and more than one answer might
be correct. The candidate gets 4 marks for selecting all the correct answers. There
is no negative marking.

Page 2

1. An arrow is released from a rigid bow at time t = 0. The magnitude of the tension
(T ) in the bowstring as a function of time is best desribed by
T

(0,0) t
A.
T

(0,0) t
B.
T

(0,0) t

C.
T

(0,0) t
D.

Page 3

2. Two air bubbles of equal initial volume rise from the bottom of a lake to the surface.
One bubble ascends and expands adiabatically while the other bubble ascends and
expands isothermally. Let VA and VT be the final volumes of the bubbles with
adiabatic and isothermal expansions, respectively. Consider an ideal gas behaviour
and note that γ is the adiabatic constant. Then,
A. VA > VT
B. VA < VT
C. VA = VT
D. VA = γVT

Page 4

3. A current I flows through a regular hexagonal loop of side length l. The magnitude
of the magnetic field at the centre is
µ0 I
A.
3πl
µ0 I
B. √
2 3πl
√
3µ0 I
C.
πl
3µ0 I
D.
πl

Page 5

4. A planet of mass m is orbiting around a non-rotating star of mass αm (α
1)
with an orbital radius r. The star ejects mass λm (λ
1) radially outwards in a
spherically symmetric fashion. Neglecting any impact of ejected mass on the planet,
the radius of new circular orbit of the planet is
A. (1 + αλ )−1 r
B. (1 − λα)−1 r
C. (1 + λα)r
D. (1 − αλ )−1 r

Page 6

5. The equivalent capacitance between P and Q for the infinite series of capacitors shown
in the figure is

√
A. C2 ( 3 + 1)
B. C3
C. 3C
√
D. C2 ( 3 − 1)

Page 7

6. The temperature and pressure at the summit of Mt. Everest is −30◦ C and 0.27 × 105
N.m−2 , respectively. The corresponding values at sea-level are 27◦ C and 1 × 105
N.m−2 . Considering air to be an ideal gas, the ratio between the molecular number
density at the summit of Mt. Everest to that at sea level is closest to
A. 1:30
B. 81:100
C. 27:100
D. 1:3

Page 8

7. Consider the following four cylindrical tubes (P,Q,R,S) all of equal radii. The tubes
Q and R are of length l. The tubes P and S are of length 1.5l. If the fundamental
frequencies are νP , νQ , νR and νS , respectively, then the correct option is

A. νR > νS > νP > νQ
B. νR > νS > νQ > νP
C. νS > νR > νQ > νP
D. νR > νP > νS > νQ

Page 9

8. A transparent glass slab of thickness t = 0.50 cm is placed with its face AB on a
horizontal table. A hemispherical water drop of radius R = 0.33 cm condenses on
the glass slab as shown in figure. The refractive indices of the slab and the water
drop are respectively 1.50 and 1.33. The image of the object at O on the face AB is
viewed after refraction from the drop. Taking OEQ as the optical axis, the distance
(cm) of the image from the point Q is

A. 1.40
B. 0.60
C. 0.72
D. 2.00

Page 10

9. A beam of monochromatic light is incident on one face of a prism√of angle 75◦ . If the
angle of incidence is 60◦ and the refractive index of the prism is 3, then the correct
option about the emergence of the beam from the opposite face is
A. no emergence.
B. grazing emergence.
C. emergence with an angle of 60◦ from the normal.
D. emergence with an angle of 30◦ from the normal.

Page 11

10. In an isobaric process involving an ideal gas the mean distance between the molecules
is quadrupled (four times). Then, the ratio of final to initial sound speeds is
A. 1
B. 2
C. 8
D. 4

Page 12

11. Two radioactive samples X and Y have the same number of atoms initially [NX (t = 0)
x
= NY (t = 0)]. The half life τ1/2 of X is half the mean life of Y . Then the ratio
x
NY (t)/NX (t) when t = τ1/2 is close to
A. 0.8
B. 1.0
C. 1.2
D. 1.4

Page 13

12. Consider the Bohr model of the hydrogen atom. Suppose that the charge of the
proton were 1.1e while the electron charge continued to be −e but the masses for
both remained unchanged. Then, the angular frequency of revolution ωB of the
electron would have
A. remain unchanged.
√
B. change to 1.1ωB .
C. change to 1.1 ωB .
D. change to 1.21 ωB .

Page 14

The following questions may have more than one correct answer. Please select all
the correct answers.

Page 15

13. A heavy disc of radius R and mass M is placed horizontally. A small coin of mass
m placed at a radial distance R/2 from the centre. The disc is now (t = 0) given a
constant angular acceleration of magnitude α rad · s−2 about a vertical axis passing
through its centre . If µs and µd are the coefficients of static and dynamic friction,
respectively, between the coin and the rotating disc, then
A. at t > 0, the force due to static friction acts radially inwards.
B. at t > 0, the magnitude of force due to static friction is always Fs = µs mg.
r
1 2µs g
C. the coin starts sliding at time t = .
α R
r
2 (µd − µs )g
D. the coin reaches the edge of the disc at time t = .
α R

Page 16

~
14. An electromagnetic wave, travelling in vacuum, is represented by E=E 0 cos(kz −wt)ŷ
where E0 is the amplitude of the electric field. A square loop of side a (a
2π/k) is
placed in its path. Then, the correct option(s) is (are)
A. B ~ = B0 cos(kz − wt)x̂ where B0 =−E0 /c
B. The wave is travelling in the y-direction.
C. The induced emf is zero if the loop lies in the xz plane.
D. The induced emf is finite if the loop lies in the yz plane.

Page 17

15. Consider the experimental set-up shown in the figure to observe the interference
pattern. Note that the prism angle θ is close to π. The correct option(s) regarding
this experiment is (are)

A. fringe width will increase with increasing angle θ.
B. fringe width will decrease with the refractive index of the lens.
C. fringe width will increase if the glass slab is lifted along y direction.
D. fringes will alternate between dark and bright if glass slab is lifted
along y direction.

Page 18

16. A current I is passing flowing through a thin copper slab placed on a diamond slab.
The bottom surface of the diamond slab is maintained at 0◦ C and the remaining
arrangment is thermally insulated from the surroundings. Note that diamond is
an excellent thermal conductor but a poor electrical conductor. Then, the correct
option(s) is(are)
A. the steady-state temperature of the copper slab is directly pro-
portional to the thickness of the diamond slab.
B. the steady-state temperature of the copper slab depends upon the specific
heat of the copper.
C. if the current is supplied from a constant voltage source, the
steady-state temperature of the copper slab will double when the
its thickness is doubled.
D. if the current is held constant, the steady-state temperature of
the copper slab will be halved if its thickness is doubled.

Page 19

17. The pair(s) with same dimensions is(are)
A. Pressure and Young’s modulus
B. Power and energy flux
C. Gravitational potential and latent heat
D. Rotational impulse and Planck’s constant

Page 20