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INDIAN FOREST SERVICE (MAINJEXAM- 2023
BJKE-U-PHY
PHYSICS
PAPER—I
Time Allowed : Three Hours Maximum Marks : 200
QUESTION PAPER SPECIFIC INSTRUCTIONS
Please read each of the following instructions carefully
before attempting questions
There are EIGHT questions in all, out of which FIVE are to be attempted.
Question Nos. 1 and 5 are compulsory. Out of the remaining SIX questions, THREE are to be
attempted selecting at least ONE question from each of the two Sections A and B.
Attempts of questions shall be counted in sequential order. Unless struck off, attempt of a
question shall be counted even if attempted partly. Any page or portion of the page left blank
in the Question-cum-Answer Booklet must be clearly struck off.
All questions carry equal marks. The number of marks carried by a question/part is indicated
against it.
Unless otherwise mentioned, symbols and notations have their usual standard meanings.
Assume suitable data, if necessary and indicate the same clearly.
Neat sketches may be drawn, wherever required.
Answers must be written in ENGLISH only.
Useful Constants :
Electron charge (e) = ` 1.602 ×10-19 ୦
Electron rest mass (716) = ` 9 .109 ×10 31 kg
Proton mass (m,) = ` 1.672 ×10 27 kg
8. 854 2९10712 farad/m
47 ×10-7 T 11 / ^
m/s ڈوو و
1. 3801023 7/௩
Vacuum permittivity (६0)
Vacuum permeability (10)
Velocity of light in free space (c)
Boltzmann constant (k)
Electronvolt (eV) = 160210-19 ౮
Planck constant (h) = 6:626x10 Js
Stefan constant (6) = 567×108 Wm ಬಗೆ
Avogadro number )7( = 6-022x1076 12011
Gas constant (R) = 831×103 ౮ 12011 1چر
exp (1) = 2-718
BJKE-U-PHY/46 1 (೫.11೮.
SECTION—A
1. (a) A particle of mass m moves under the action of a central force whose potential
is V(r) = Kmr* (ਨ > 0). Calculate the kinetic energy for which the orbit will be
circle of radius R, about the origin. 8
(b) What are the coordinates of the centre of mass of the system of masses shown
in the figure?
8 kg
12 ਨ
y(m)
4kg
1 772
3 kg
711 1 2
x(m) —> ৪
(c) Calculate the velocity of a particle having kinetic energy four times the rest
mass energy. 8
(d) Explain with proper examples the techniques of obtaining interference by
‘division of wavefront’ and ‘division of amplitude’. 8
(e) A length of 25 cm of a solution containing 50 gm of solute per litre causes a
rotation of the plane of polarization of light by 5°. Find the rotation of the plane
of polarization by a length of 75 cm of the solution containing 100 gm of solute
per litre. 8
2. (a) A hoop is rolling down on an inclined plane without slipping. Find its velocity
at the bottom of the inclined plane. 15
(b) Calculate the inertia tensor for a rigid body consisting of three particles of
masses 3 gm, 1 gm, 2 gm located at (1, -1) 2) ୦୮୮, (1,0,2)cm, (-2,1,0)cm
respectively. 15
(c) Define Einstein’s coefficients A and B for spontaneous and stimulated
emissions, and write the relation between them. If the Einstein’s coefficient of
spontaneous emission is 107/8, determine the Einstein’s coefficients for the
stimulated emission for the emission wavelength of 5800 A. 5+5=10
BJKE-U-PHY/46 2
3. (a) Consider a thick equiconvex lens of refractive index 1-5 as shown in the figure.
The magnitude of the radii of curvatures of the two surfaces is 5cm. The
thickness of the lens is 1 cm and the lens is placed in the air. Obtain the
system matrix and determine the focal length and the position of unit planes :
ঙ ല് 3 15
(b) Ina reference frame 5, an event 1 occurs at the origin at t=O and another
event 2 occurs at x = 4000 m and time £ = 5 × 10 6 s. Find the time interval
between the events as registered by clock in a frame S’ moving with speed
v=0-6c relative to 5 along the common X-X’ axis, the origin coinciding at
t=t’=0. 10
[ष
© ட Explain an experiment for determination of the refractive index of a gas
using Michelson interferometer. 9
8 In the above experiment, a shift of 100 fringes is obtained when all the gas
is removed from the tube. Calculate the refractive index of the gas if the
wavelength of light used is 6000 A and the length of the tube is 10 cm. 6
4. (૦) Anachromatic doublet of focal length 25 cm is to be made by placing a convex
lens of borosilicate crown glass in contact with a diverging lens of dense flint
glass. Assuming ہہ = 1. 61864, ಗ್ಯ =1-62468, 7/ = 1. 71426 and یہ =1-72906,
calculate the focal length of each lens. Here, the unprimed and the primed
quantities refer to the borosilicate crown glass and dense flint glass
respectively. 15
(b) Find an expression for the average energy of a forced oscillator in the
steady-state motion. 10
(c) Explain the formation of spectra by a plane diffraction grating. What particular
spectra would be absent if the width of the slit is equal to the width of the
opaque spacing between any two consecutive slits? 15
BJKE-U-PHY/46 3 [ ೫:1೦,
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6. (a)
(b)
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(b)
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SECTION—B
Why does a neutron star have a magnetic field if it is composed of neutrons?
What is the concept of negative temperature in statistical mechanics? Explain
in brief.
Explain Ampere’s circuital law of magnetic field. What modifications Maxwell
made in this equation to derive Maxwell’s fourth equation?
Assuming that the Sun radiates like a perfect blackbody, at what wavelength
does the peak of the solar spectrum occur? Given that the surface temperature
of the Sun is about 6000 K.
If the electrostatic potential in spherical polar coordinate is
$7) 006 7/0
where $9 and 70 are constants, what will be the charge density at a distance
7-70?
Distinguish between a perfect gas and a real gas. Derive van der Waals’
equation of state and use it to obtain the expressions for the critical constants
in terms of the constants of the van der Waals’ equation.
Explain how we can produce refrigeration without using a compressor.
Write down Stefan-Boltzmann law of radiation and derive it from Planck’s law
of radiation.
Write down the electromagnetic wave equation in non-conducting dielectric
medium. Hence, show that the velocity of wave propagation is given by v = க
where the symbols have their usual meanings.
A material has ೮ = 1072 S/m and ੬ = 2६0. At what frequency, the conduction
current would be equal to the displacement current?
An infinitely long coaxial cylinder structure has an inner conductor of radius a
and an outer conductor of radius ల. The inner conductor is attached to Vo,
while the outer one is grounded. Calculate the field E in between a and b.
BJKE-U-PHY/46 4
15
10
15
15
10
8. (a) What is Lenz’s law? Is Lenz’s law the same as Faraday’s law? What happens if
Lenz’s law is reversed? Explain. 15
(b) The wire AB shown in the figure below has mass m, resistance r and it can
slide on the smooth horizontal parallel rails separated by a distance 1.
A uniform magnetic field B exists in the rectangular region and a resistance R
connects the rails outside the field region. At t=0, the wire AB is pushed
towards right with a speed vo.
x ౫ இ ਨ x x
Find out the current in the loop at an instant when the speed of the wire is v.
Find out the velocity v as a function of x. (Assume that the resistance of the
rails is negligible) ৷ 10
(c) Explain how the state of ionization of any particular element in a star changes
with varying temperatures and pressures. 15
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BJKE-U-PHY / 46 5 SB24—138
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