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Indian Forest Services (Main)
Examination-2025 DJSM-U-PHYS
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.
Questions no. 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 x 10-19 C
9-109 x 10-81 kg
Electron rest mass (m,)
Proton mass (m,) = 1672x1027 kg
Vacuum permittivity (9) = 8-854 x 10-!2 farad/m
Vacuum permeability (11g) = 41x10? TmV/A
3 x 108 m/s
1-380 x 10-23 J/K
Velocity of light in free space (c)
Boltzmann constant (k)
Electronvolt (eV) = 160210195
Planck constant (h) = 6626x104 Js
Stefan constant (0) = 567x108 Wm? K+
Avogadro number (N) = 6-022 x 1026 kmol-!
Gas constant (R) = 831x103 J kmol-! K"}
exp (1) = 2-718
DJSM-U-PHYS 1
Ql. (a)
(b)
(c)
(d)
(e)
Q2. (a)
(b)
(c)
SECTION A
Two particles each of rest mass 1 gm collide head-on with the speed
0-8c to stick together at rest. Find the mass of the final composite.
Calculate the effective gravitational acceleration at the equator due to
the Earth’s rotation. [Rearth = 6400 km]
A 15-0 cm violin string, fixed at both the ends, is vibrating with the
largest wavelength. The speed of the wave in this string is 250 m/s, and
the speed of sound in air is 350 m/s. What is the frequency and
wavelength of the emitted sound wave ?
Determine the position of focal points, principal points and nodal points
for a spherical lens of radius 20 cm. The refractive index of the material
of the lens is 3/2. Indicate the positions of all the points in a diagram.
A parallel beam of sodium light of wavelength 5893 A is incident on a
diffraction grating. The angle between the first order spectra on either
side of the normal is 27°42".
Find : 44+4=8
(i) The number of rulings/mm on the grating.
(ii) The greatest number of bright images obtained.
A particle of mass m is suspended from a spring which has mass m and
force constant k. Show that the oscillation frequency is given by
B
® = —®@®g, where @g is frequency of oscillation when spring is
2 0 0
considered massless.
A particle of mass m moves under the attractive central force
fo
potl
. Find the condition for which the particle will have stable
circular orbit. (C > 0, a constant).
Explain the construction and working of a quarter-wave plate. How is it
used to produce circularly and elliptically polarized light ? 8+2=10
DJSM-U-PHYS 2
Qs.
(a)
(b)
(c)
(a)
(b)
(c)
(i) Define cyclic coordinates and find their connections with the
symmetries of the system.
(ii) A system with two degrees of freedom is described by the
< 1 . 1 . a .
Lagrangian L = Pact ay + 54 a - % , a is constant.
Find the cyclic coordinates, conserved quantities and symmetries
for this system, if any. 10+5=15
Consider two inertial frames S and S’.. S’ is moving along
y-direction with a constant speed vg. Find how the first order partial
derivatives with respect to x, y, z and ct are connected in these two
inertial frames. Show that the D’Alembertian, V2 — soon. is invariant
ea
under the Lorentz transformation. 15
Within the framework of the Cornu’s spiral, describe the intensity
distribution at an arbitrary point P when a plane wave is incident
normally on a long narrow slit of width b.
For this case, under what condition will the diffraction pattern be of
Fraunhofer type ? 8+2=10
Describe the interference by a plane parallel thin film when illuminated
normally and obliquely by a plane wave.
Also list some important practical applications of the thin film
interference phenomenon. 8+2=10
What do you understand by pulse dispersion in multimode optical
fibres ? Deduce an expression for intermodal pulse dispersion in a
step-index fibre. Also compare the pulse dispersions of the step-index
fibres with the parabolic-index fibres. 10+5=15
Write down the Euler equations for torque-free motion of a rigid body.
Solve these equations to find precessing motion for a symmetric top. 15
DJSM-U-PHYS 3
SECTION B
Q5. (a) After highlighting the importance of the Biot-Savart law, show that the
magnetic field of a current carrying long wire, at a point near it, is
inversely proportional to the distance of the point from the wire.
(b) A certain linear, homogeneous, isotropic, dielectric material has a
relative permittivity, ¢. = 1-8. If potential V = — 4000y volts in the
material, then find :
(i) The electric flux density D, and
Gi) The polarisation P.
Take vacuum permittivity ¢9 = 8-85 x 10-!2 farad/m.
(c) Consider that an ideal non-interacting Fermi gas with internal energy
U’ at temperature T is kept in a cubical box of volume V. Find the
pressure for the gas in terms of U and V.
(d) Fora plane electromagnetic wave given by :
E, = a cos @x cos oct
Hy =—a sin ox sin oct
Find the value of the Poynting vector.
(e) For silver, the specific heat at constant pressure in the range of 50 K to
100 K is given by :
C, = 0-076 T - 0-00026 T? — 0-15 cal mol ‘deg!
If 2 moles of silver are heated from 50 K to 100 K, calculate the change
in entropy.
DJSM-U-PHYS 4
10060
12/5
Poisson’s equation, find potential V(r). It is assumed that 12 E, > 0
Q6. (a) Ifvolume charge density in free space varies as = , then using
when r > 0, while V > 0 at 1 -> . 10
) What is the method of images ? What are the conditions which
must be satisfied while applying the method of images to deal
with electrostatic problems ?
(ii) A point charge Q is located at the point (a, 0, b) between two
semi-infinite conducting planes intersecting at right angles as
shown in the figure. Using the method of images, determine the
potential at point P(x, y, 2) in the region z > 0 and x > 0 and the
force on Q. 5+10=15
Z
ae
4
4
4
4 a Q
| |
4
4
b
20 |
0 ^ x
Figure
(60 ) Show that the vector potential 2 at the position defined by
the vector r in a uniform electric and magnetic field is
>
A = $ 0 7).
(1) out the divergence and curl of the vector potential £. 5470-75
DJSM-U-PHYS 5
Q7. (a) For the following series LCR circuit,
04H O4nF 102
L C R
Calculate :
(i)
(ii)
(iii)
(iv)
The resonant frequency of the circuit.
The maximum current in the circuit.
The voltage across C at resonance.
The power absorbed by the circuit at resonance.
(b) | Deduce Fresnel’s law for the propagation of plane electromagnetic waves
through an anisotropic dielectric medium.
(c) One gram of water (1 cm?) becomes 1671 cm? of steam when boiled at
constant pressure of 1 atm (1:013 x 10° Pa). The heat of vapourization at
this pressure is L = 2-256 x 108 J/kg.
Calculate :
(i)
(ii)
Q8. (a (i)
DJSM-U-PHYS
The work done by the water when it vapourizes, and
Increase in its internal energy.
Assuming the Maxwell’s velocity distribution formula, find out the
value of :
(A) Mean velocity (¥),
(B) The most probable velocity (vmp), and
(C) Root mean square speed (vrms)
in terms of the Boltzmann constant (kp) and show that :
Vrms > V > Vmp-
15
15
10
(ii) If nitrogen molecules are kept at 27°C, find out the value of
Vrms » V and Vmp.-
Given : Molecular mass of nitrogen M = 28 x 10° kg/mol and gas
constant R = 8-314 J.mol 1K}. 15+5=20
(b) Consider N non-interacting ideal spinless particles (Bose gas) are
occupying a volume V. Find out the temperature ‘T’ below which B-E
condensation takes place. 10
(c) Assume the Sun to be a black body at temperature 5800 K. Use Stefan’s
law to calculate :
(i) The total energy emitted by the Sun per second, and
(ii) |The energy reaching the top of the Earth’s atmosphere.
Given : o = 5-672 x 10°8 SI units,
Radius of the Sun = 7 x 108 m,
The distance of the Earth’s atmosphere from the Sun = 1:5 x 1011 m. 10
DJSM-U-PHYS 7
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