Exam Details
| Subject | physics | |
| Paper | paper 1 | |
| Exam / Course | indian forest service | |
| Department | ||
| Organization | union public service commission | |
| Position | ||
| Exam Date | 2012 | |
| City, State | central government, |
Question Paper
[Indian Examination-201 ......,
D-GT-M-QIAJ
I
PHYSICS
Paper-I
Time Allowed: Three Hours) (Maximum Marks 200)
INSTRUCTIONS
Candidates should attempt Question Nos. I and 5 which are compulsory, and any THREE of the remaining questions, selecting at least ONE question from each Section. All questions carry equal marks. The number of marks carried by each part of a question is indicated against each. Answers must be written in ENGLISH only. Assume suitable data, if necessary, and indicate the same clearly. Unless otherwise indicated, symbolic notations carry usual meaning. Important Note All parts/sub-parts of a question must be attempted contiguously. That is, candidates must complete attempting all parts/sub-parts of a question being answered in the answer-book before moving on to the next question. • Pages left blank, if any, in the answer-book must be clearly struck out. Answers that follow pages left blank may not be given credit.
Useful Constants
Electron charge I·6Q2xi0-19 C
Electron rest mass 9·109x 10-31 kg e
Proton mass 1·672xlo-27 kg
p
Vacuum permittivity 8·854X I o-12 farad/m
Vacuum permeability (J.I 1·257x I 0-6 henry/m
Velocity of light in free space 3xiQ8 m/s
Boltzmann constant 1·38xJ0-23 J/K
Electron volt 1·6Q2x1Q- 19 J
Planck's constant
Stefan's constant cr)
Avogadro's number
Gas constant
6·62x I o-34 J-s
5·67xi0-8 W m-2 K-4
6·02x I o2 6 kmor1
8·31 X I 03 J kmol- 1 K-1
2·7183 exp
SECTION-A
I. Answer the following 8x5=40
Express Lagrange's equation of motion for the cyclic coordinate q. and show that the result leads to the general conservation theorem for the generalized momentum coordinates.
Using the concept of the operator equation for a given vector quantity of a rotating body, show that vs vt+wxr where vs and vr are the velocities of the particle relative to space and rotating sets of axes while w is the angular velocity of the earth relative to the inertial system. Obtain the expression for the Coriolis force for such a moving system of mass m.
A man has a mass of 100 kg on earth. When he is on the space craft an observer from the earth registers his mass as I 02 kg. Determine the speed of the space craft.
Two lenses of focal lengths 8 cm and 4 cm are placed at a certain distance apart. Calculate the distance between the lenses if they form an achromatic combination.
A step-index silica fiber consists of core of refractive index 1·450 and diameter 90 um. If the numerical aperture of the fiber is 0·16, calculate the acceptance angle of the fiber, refractive index of the cladding, and if the fiber is immersed in water of refractive index 1·33, how does the acceptance angle change
2. Starting with Newton's second Jaw of motion, establish Alembert's principle and discuss its significance. 8
Using AI em bert's principle, show that the
following relation can be obtained for a system
of particles under generalized coordinates
" F· ·or:=" Q· oq· I I L..J J J
i j
" i3T: with Qj L..- Fi .
. i3q·
" I J
What is the significance of Q.
. J .
•
16
(Contd.)
www.examrace.com
State Hamilton's principle for the motion of a
monogenic system.
Use the calculus of variation to deduce
Lagrange's equation that follows from Hamilton's
principle. Explain carefully all the terms used in
the derivation. 16
3. Explain mathematically the plienomenon Of beats.
How does it differ from that of interference 15
When two tuning forks were sounded together,
24 beats were produced in 6 seconds. After loading
one tuning fork with wax, they produced 30 beats
in 6 seconds. If the unloaded fork frequency is
512, what is the frequency of the other 15
A body describing simple harmonic motion
has a maximum acceleration of 8 nm/sec2 and a
maximum speed of 1·6 m/sec. Find the time period
and the amplitude of SHM. 10
4. Explain the Fraunhofer diffraction at a single slit
and obtain the condition for minima. Derive the
expression for resolving power of a grating. 15
An optical waveguide has core and cladding of
refractive indices 1·46 and 1·45 respectively.
Calculate the maximum number of modes
with wavelength A. 900 nm that can travel
if it is a planar waveguide of core thickness
I 0 1.1m.
(Contd.)
www.examrace.com
What is the number of modes if it is a
cylindrical fiber of diameter I 0 Jlm I 0
What are Einstein's A and B coefficients? Establish
a relation between them.
SECTION-B
5. Answer the following
15
8x5=40
Show that the complex propagation constant k of
an electromagnetic wave propagating in an
isotropic dielectric medium with conductivity cr
can be given by k k ik. with r 1 ..
2 2 A.. 8
and
2
1t n .!. A.. 2
where n and .A.. ro/21tc; and c being
the permittivity of the dielectric and velocity of
light in free space, respectively.
Explain the physical significance of the
Poynting vector S. What is represented by the
closed integral f S · da for a closed surface of
area a
(Contd.)
www.examrace.com
•
Explain the thermodynamic behaviour of an ideal
Fermi gas. What are fermions
Show that if an ideal gas is compressed
isothermally its compressibility is whereas if
p ..
it is compressed adiabatically its compressibility
I .
is where y C IC . yp p v
The dielectric constant of a medium is 3. The
Electric field in the dielectric is 1 06 V m-I. What
are the electric displacement and polarization
6. Explain the term 'mutual inductance' between two
coils carrying current. Describe a method of
determining mutual inductance between two coils
of wire with relevant theory. 20
A long straight solenoid has 100 turns in the
secondary and 3 000 turns per centimeter in the
primary. The area of cross-section of the solenoid
is 3 square centimeters. Calculate the mutual
inductance. 15
How do you justify the statement "A current
carrying conductor, although has no net charge
experiences a force when placed in a magnetic
field." 5
(Contd.)
www.examrace.com
· 7. If considered a blackbody as a radiation-filled
cavity at a uniform temperature demonstrate
with an appropriate figure the. electromagnetic
wave patterns inside the cavity of length L for
8.
3
wavelengths f.. 2 L and 2L. ·· I 0
For the above system, show that the energy per
unit cavity volume in the frequency range of
v and v dv can be given by
8nv 2 k 8 T d uv 3 v
c
where k
8
is the Boltzmann's constant. Discuss
the limitations of this formula and how did Planck
put forward the correct analysis. 20
Find out the number of photons in a cavity of
volume I ·00 cm3 under thermal equilibrium at
temperature T 1000 °K.
Assume that
"" 2 f x dx 2·405.
0
ex
Derive the gas equation when it
adiabatic process.
10
undergoes
10
(Contd.)
www.examrace.com
A motor car tyre has . a pressure of
2 atmospheres at the rooin .temperatu_re of 27°C.
If the tyre suddenly bursts, ·find the resulting
· temperature. 10
What are bosons Based, on
statistics, derive the expression for Bose-Einstein
condensation. 15
Find the efficiency Camot's engine _working
between 127°C and 27°C. 5
•
•.
...._ •• . ..
•
.
www.examrace.com
D-GT-M-QIAJ
I
PHYSICS
Paper-I
Time Allowed: Three Hours) (Maximum Marks 200)
INSTRUCTIONS
Candidates should attempt Question Nos. I and 5 which are compulsory, and any THREE of the remaining questions, selecting at least ONE question from each Section. All questions carry equal marks. The number of marks carried by each part of a question is indicated against each. Answers must be written in ENGLISH only. Assume suitable data, if necessary, and indicate the same clearly. Unless otherwise indicated, symbolic notations carry usual meaning. Important Note All parts/sub-parts of a question must be attempted contiguously. That is, candidates must complete attempting all parts/sub-parts of a question being answered in the answer-book before moving on to the next question. • Pages left blank, if any, in the answer-book must be clearly struck out. Answers that follow pages left blank may not be given credit.
Useful Constants
Electron charge I·6Q2xi0-19 C
Electron rest mass 9·109x 10-31 kg e
Proton mass 1·672xlo-27 kg
p
Vacuum permittivity 8·854X I o-12 farad/m
Vacuum permeability (J.I 1·257x I 0-6 henry/m
Velocity of light in free space 3xiQ8 m/s
Boltzmann constant 1·38xJ0-23 J/K
Electron volt 1·6Q2x1Q- 19 J
Planck's constant
Stefan's constant cr)
Avogadro's number
Gas constant
6·62x I o-34 J-s
5·67xi0-8 W m-2 K-4
6·02x I o2 6 kmor1
8·31 X I 03 J kmol- 1 K-1
2·7183 exp
SECTION-A
I. Answer the following 8x5=40
Express Lagrange's equation of motion for the cyclic coordinate q. and show that the result leads to the general conservation theorem for the generalized momentum coordinates.
Using the concept of the operator equation for a given vector quantity of a rotating body, show that vs vt+wxr where vs and vr are the velocities of the particle relative to space and rotating sets of axes while w is the angular velocity of the earth relative to the inertial system. Obtain the expression for the Coriolis force for such a moving system of mass m.
A man has a mass of 100 kg on earth. When he is on the space craft an observer from the earth registers his mass as I 02 kg. Determine the speed of the space craft.
Two lenses of focal lengths 8 cm and 4 cm are placed at a certain distance apart. Calculate the distance between the lenses if they form an achromatic combination.
A step-index silica fiber consists of core of refractive index 1·450 and diameter 90 um. If the numerical aperture of the fiber is 0·16, calculate the acceptance angle of the fiber, refractive index of the cladding, and if the fiber is immersed in water of refractive index 1·33, how does the acceptance angle change
2. Starting with Newton's second Jaw of motion, establish Alembert's principle and discuss its significance. 8
Using AI em bert's principle, show that the
following relation can be obtained for a system
of particles under generalized coordinates
" F· ·or:=" Q· oq· I I L..J J J
i j
" i3T: with Qj L..- Fi .
. i3q·
" I J
What is the significance of Q.
. J .
•
16
(Contd.)
www.examrace.com
State Hamilton's principle for the motion of a
monogenic system.
Use the calculus of variation to deduce
Lagrange's equation that follows from Hamilton's
principle. Explain carefully all the terms used in
the derivation. 16
3. Explain mathematically the plienomenon Of beats.
How does it differ from that of interference 15
When two tuning forks were sounded together,
24 beats were produced in 6 seconds. After loading
one tuning fork with wax, they produced 30 beats
in 6 seconds. If the unloaded fork frequency is
512, what is the frequency of the other 15
A body describing simple harmonic motion
has a maximum acceleration of 8 nm/sec2 and a
maximum speed of 1·6 m/sec. Find the time period
and the amplitude of SHM. 10
4. Explain the Fraunhofer diffraction at a single slit
and obtain the condition for minima. Derive the
expression for resolving power of a grating. 15
An optical waveguide has core and cladding of
refractive indices 1·46 and 1·45 respectively.
Calculate the maximum number of modes
with wavelength A. 900 nm that can travel
if it is a planar waveguide of core thickness
I 0 1.1m.
(Contd.)
www.examrace.com
What is the number of modes if it is a
cylindrical fiber of diameter I 0 Jlm I 0
What are Einstein's A and B coefficients? Establish
a relation between them.
SECTION-B
5. Answer the following
15
8x5=40
Show that the complex propagation constant k of
an electromagnetic wave propagating in an
isotropic dielectric medium with conductivity cr
can be given by k k ik. with r 1 ..
2 2 A.. 8
and
2
1t n .!. A.. 2
where n and .A.. ro/21tc; and c being
the permittivity of the dielectric and velocity of
light in free space, respectively.
Explain the physical significance of the
Poynting vector S. What is represented by the
closed integral f S · da for a closed surface of
area a
(Contd.)
www.examrace.com
•
Explain the thermodynamic behaviour of an ideal
Fermi gas. What are fermions
Show that if an ideal gas is compressed
isothermally its compressibility is whereas if
p ..
it is compressed adiabatically its compressibility
I .
is where y C IC . yp p v
The dielectric constant of a medium is 3. The
Electric field in the dielectric is 1 06 V m-I. What
are the electric displacement and polarization
6. Explain the term 'mutual inductance' between two
coils carrying current. Describe a method of
determining mutual inductance between two coils
of wire with relevant theory. 20
A long straight solenoid has 100 turns in the
secondary and 3 000 turns per centimeter in the
primary. The area of cross-section of the solenoid
is 3 square centimeters. Calculate the mutual
inductance. 15
How do you justify the statement "A current
carrying conductor, although has no net charge
experiences a force when placed in a magnetic
field." 5
(Contd.)
www.examrace.com
· 7. If considered a blackbody as a radiation-filled
cavity at a uniform temperature demonstrate
with an appropriate figure the. electromagnetic
wave patterns inside the cavity of length L for
8.
3
wavelengths f.. 2 L and 2L. ·· I 0
For the above system, show that the energy per
unit cavity volume in the frequency range of
v and v dv can be given by
8nv 2 k 8 T d uv 3 v
c
where k
8
is the Boltzmann's constant. Discuss
the limitations of this formula and how did Planck
put forward the correct analysis. 20
Find out the number of photons in a cavity of
volume I ·00 cm3 under thermal equilibrium at
temperature T 1000 °K.
Assume that
"" 2 f x dx 2·405.
0
ex
Derive the gas equation when it
adiabatic process.
10
undergoes
10
(Contd.)
www.examrace.com
A motor car tyre has . a pressure of
2 atmospheres at the rooin .temperatu_re of 27°C.
If the tyre suddenly bursts, ·find the resulting
· temperature. 10
What are bosons Based, on
statistics, derive the expression for Bose-Einstein
condensation. 15
Find the efficiency Camot's engine _working
between 127°C and 27°C. 5
•
•.
...._ •• . ..
•
.
www.examrace.com