I.F.S. EXAM-2015
C-GEQ-0-QIZA

PHYSICS

PAPER-I

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
q..estion 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.

.. questions carry equal marks. The number of marks carried by a question/part is
indicated against it.
Answers must be written in ENGLISH only. •
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.

Useful Constants

Electron charge J. 602 x 10-19 C
Electron rest mass 9 -109 X l0-3l kg


e

Proton mass l · 672 X 10-27 kg
Vacuum permittivity 8· 854 x 10-12 farad/m
Vacuum permeability 1-257x10-6 hemy/m
Velocity of light in free space 3xl08 m/s
Boltzm..nn constant (kl l-380x10-23 J/K
Electroiwolt 1-602xl0-19J
Planck constant 6· 626 X 10-34 JS
Stefan constant 5-67x 10-8 wm-2 K-4
Avogadro number 6 · 022 x 1026 kmol-1
Gas constant 8·31x 103 Jkmol-1 K-1
exp 2•718


1 [P.T.O.



f

SECTION-A

1. Answer all of the following
8x5=40

The Lagrangian for a particle has the form
· L

2

Obtain its form in plane polar coordinates and then get expression for the
Hamiltonian using appropriate transformation.


Discuss that the motion of a particle in a central field gets restricted to a plane
provided its angular momentum is nonzero. What will happen if the angular
momentum is zero?
Find the velocity and momentum of a particle having rest mass m0 and kinetic
energy equal to two times of its rest mass energy.


In Young's double-slit experiment, a thin mica sheet (refractive index= 1 · is
introduced in the path of one of the beams. If the central fringe gets shifted by
0·2 cm, calculate the thickness of the mica sheet. Assume separation between
the two slits and between slit and source as d 0 · 1 cm and D 50 cm.

Explain physically why dispersion is diminished in multimode parabolic-index
fiber than in step-index fiber .
•

2.
Obtain the equation of motion of a simple pendulum using Lagrangian
formalism. Hence, obtain expression for the angular frequency of a simple
harmonic oscillator. 15

A particle of mass m is moving with the velocity v on the surface of the earth.
Discuss the nature of its motion in both the hemispheres due to the




Coriolis force F m ro X 0.
15


Solve Euler's equation of motion for a rigid body to show that the torque-free
motion of a spherical top is a uniform rotation about an axis fixed in space. 10
3. Describe briefly the Michelson-Morley experiment and discuss the significance
of its null result in the context of the special theory of relativity. 15
. Viewing ionosphere as a dielectric medium of refractive indexµ ..1 -ro.. ro 2


c.o being known as the plasma frequency, determine the group velocity of a
P

radio wave of frequency co ./2.ro .

P
1o


Explain, with neat diagrams, what you mean by monochromatic spherical
aberration with reference to paraxial focus, marginal focus and circle of least
confusion. 15
2



4. With a planoconvex lens of radius of curvature R resting on a plane glass
surface, Newton's rings are observed with incident light of wavelength 11.. Find
the radii of mth order dark rings. What will be the colour of the innermost ring
with white light illumination? 10
Deduce an expression for resolving power of a diffraction grating, explaining its
meaning. What will be the value of the number of slits in the grating to resolve
D1 and D2 lines of sodium in the first order, assuming A and flA respectively as
600 nm and 0·6 nm? 15
Explain the refractive index distribution for
given as
a graded index optical fiber
n2
• nf(1 r a
nf n.. r a
with usual meaning of symbols. Sketch and name the above profiles with
justification for q 2 and oo. 15

15
[P.T.0.
I
j
i I
SECTION-B

S. Answer all of the following
8x5=40

Verify whether the electric potential V 15x2 yz -5y3 z satisfies Laplace's
equation or not.

In a simple AC circuit involving only a resistor R 50 n and a voltage
source find the linear frequency of the generator if V 0 · 5 VWm is peak
e.m.f.) at time {assuming V=O at O).
m
720

Which of the Maxwell equations imply that there are no magnetic monopoles?
Explain how the equations would get modified if magnetic monopoles would

.exist.


Discuss the consequence following from Joule's free expansion experiments in
the context of the internal energy of an ideal gas.

Plot the Fermi distribution function versus energy at temperatures T 0 and
T 0. Explain the nature of the former curve on the basis of the Pauli principle.
6.
The electric potential of a grounded conducting sphere of radius a in a uniform
electric field E E0z is given as
Find the expression for the surface charge density on the sphere.
3


Using Ampere's law, derive the magnetic field of a toroid turns each carrying
current of inner radius a and outer radius bat a distance r midway between
a and b. 10

A plane conducting circular wire loop lies perpendicular to a uniform magnetic

field Band its area is changed as where O t (S0 and a
a


are
constants). The wire has resistance per unit length p Q m -1. Find the

induced current through the wire.

If the current in a certain coil varies at a rate of 50 the induced e.m.f. is

V 20 volts. What is the inductance of the coil?
10+5

7.
Prove that the work done on the charges by the electromagnetic force is equal
to decrease in energy stored in the field, less the energy that flowed out
through the surface.
Explain what you mean by the Poynting vector.
20+5


Discuss the physical significance of Planck's radiation law in the context of
emergence of New Physics.
If the blackbody energy density has a functional dependence like
x 3 (ex -1r1
where x 1iw, derive Wien's displacement law and·comment

kT

on its importance.
5+10 ·1

8.
Start from the equation
TdS Cp dT dP

ar P



and get the relation
..· .. "I



a2


2

aP
r

ar

p

Hence, show that the third law of thermodynamics requires for the coefficient
of thermal expansion of any substance to vanish at T 0. 15


Derive an expression for the total number of particles Nin an ideal Bose gas at
any temperature T. Hence, obtain the relation
for the number of particles NO in the ground state at T T0, the Bose-Einstein
condensation temperature; and draw N0 versus T curve. 10+ 10



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SB6-190