Exam Details
| Subject | physics | |
| Paper | paper 1 | |
| Exam / Course | indian forest service | |
| Department | ||
| Organization | union public service commission | |
| Position | ||
| Exam Date | 2014 | |
| City, State | central government, |
Question Paper
lNDlAN FOREST SERVlCE P lEYJiM}?SJt..
jC-HENT-N-YPNMAj
PHYSICS
ITime Allowed Three Hours I IMaximum Marks 20Q I
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 Sare compulsory. Out of the remaining SIX questions, THREE are to be attempted I
selecting at least ONE question from each of the two Sections A and B.
All questions carry equal marks. The number of marks carried by a part of a question 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.
All parts and sub-parts of a question are to be attempted together in the answer book.
Any page .or portion of the page left blank in the Answer Book must be clearly struck out.
Useful Constants
Electron charge 1.602 x 10-19 C
Electron rest mass 9.109 X 10-JI kg
Proton mass 1.672 X 10-:27 kg
p
Vacuum permittivity 8.854 x 10-12 farad/m
Vacuum permeability l.257 x 10-6 henry/m
Velocity of light in free space 3 x 108 mis
Boltzmann constant 1.38 x 10-23 J/K
Electron volt J.602 X 10-19 J
Planck's constant 6.62 X 1 o-J4 J-S
Stefan's constant 5.67 x 10-s wm-2 K-4
Avogadro's number 6.02 x 1026 kmol-1
Gas constant 8.31 x 103 J kmot-1 K-1
exp 2.7183
C-HENT-N-YPNMA
000
SECTION-A
Q. 1. Answer the following
8X5=40
Q. Using the concept ofD'Alembert's principle, show that the generalized force can be defined as <img src='./qimages/1297-1a.jpg'> where ri is the Cartesiflll coordinate of the ith particle experiencing external force Fi and qj stands for the generalized coordinate. Discuss the significance of the above expression.
Q. Write down the mathematical representation of Fermat's principle and explain all the notations used.
With the help of a neJt diagram, show that this principle can be used to· obtain the law of refraction
n1 sino1=n2 sin02.
where n1 and n2 are th.. refractive indices of the two media while 8and 82 are the angles of incidence and refrabtion of the light.beam. 8
Q. If the system matrix for a thin lens of focal length f is given by
o
show that the system rpatrix for a combination of two thin lenses of focal lengths fand f2 separated by a distance d can be obtained as
<img src='./qimages/1297-1c.jpg'>
Q.l(d) A left circularly polarized beam 5893°A) is incident normally on a calcite crystal (with its optic axis cut parallel to the surface) of thickness 0.005141 mm. What will be the state of polarizaticln of the emergent beam Ju..tify your answer. Here the refractive indices for t..e ordinacy and the extraordinary rays are l.65836 and 1.48641 respectively.
Q. Deduce the minimum.lnergy.of a·gamma ray photon (in which can cause electro: positron pair production. 8
Q. State Hamilton's principle for a system of particles. If I and L represent the action integral and the Lagrangian furiction,·respectively, write down.the mathematical form ofHainilton's principle and explain /clearly the significance of the same. 15
Q. Discuss the torque-free motion of a symmetric rigid body and hence estimate the period of precession of Earth's polar axis. [Use i3-i1/i3 =0.33, where i1, i2 and i3 are the moments of inertia about the 1Le principal axes the Earth] 15
Q. A particle o..rest mass M moving at a velocity u cQllides with a stationary particle of rest ·
mass m. If the particles stick together, show that the speed of the composite ball is equal
<img src='./qimages/1297-2c.jpg'>
Q. Derive the law of addition of relativistic velocities. Us_e it to prove that under the Lorentz
transformation no two velocities can add upto more. than tbe value of the speed of iight. 15
Q. Starting with the rate equations for matter-radiation interaction, show that the ·ratio of the Einstein's A and B coefficients is proportional. to the third power of the frequency of radiation. 15
Q. How does the population inversion in an active medium lead to the amplification of light .in a laser Explain in details.
Q. Explain how you can construct a zone plate from Fresnel's half perfod zone. Show that a zone plate has multiple foci. 15 .
·Q. What are the step index andgraded index optical ·fibers · · What ·are the conventional optical windows for light propagation through optical fibers l 5
Q. Draw a neat diagram to show how light propagates through a graded index optical fiber ·
from the entrance to the fiber end and explain. 10
SECTION-8
Q. 5. Answer the following
8XS=40
Q. Prove Stefan'.. law of radiation from thennodyn..ic considerations. 8
Q. For a degenerate Fermi-Di_rac gas. the concentration of nucleons .in nuclear matter is N 1.1 x 1038 cm-3• Calculate the· Fermienergy and Fermi temperature.. 8
Q. Suppose a cavity of vol..me V contains biackbody radiation in equilibrium with the walls of the cavity at a temperature T. For a reversible adiabatic change of volume show that VT3 constant. If the initial temperature is 2000°K and the volume is incre_ased-fro.. _10 cm3 to 1250 c m3, reversibly and adiabatically, what would be the final temperature of the radiation 8
Q. Compute the electrostatic energy of a conducting solid sphere of radius R and having the total charge q using the expression for the electrostatic energy in terms of the electric field e of the above sphere.
Q.5(e) Show that the elemental !quantity of heat dQ is not a total differential.field E of the above sphere. 8
Q.6(a) Explain Kirchoff's circuit laws. Using Kirchooffs laws find currents I1, I2 and I3 in the
circuit shown below for R1= 100 R2 200 omegha R3= 300omegha E1= 3 E2= 4 V.
<img src='./qimages/1297-6a.jpg'>
q.6(b).An inductance capacitance C and resistance Rare connected iwith AC source driving Jith Erms 120 V at
f=60 Hz. Compute the power factor and
average power dissipated;in the resistance if R 200 XL 80 Q and Xc= 150omegha.
Q A sphere of homogeneous linear dielectric material is placed in an otherwise uniform electric field E0 Find th.. electric field inside the sphere. 15
Q. A plane electromagnetic +ave of frequency w1 travelling in z-direction and polarized in
x-direction is incident on ·a dielectric medium separatecl by a plane boundary in the x-z
plane. Show that the tranfmission and reflection coefficient are given by
<img src='./qimages/1297-7a.jpg'
where n1 and n2 are the refractive indices of the first a,nd the second medium. 20
Write Maxwell's equations in the absence of a medium.
Explain the gauge transformation and gauge invariance. Show that the relation
div A +1/cdelta0/deltat is Lorentz-covariant, where A and are the vector potential and the scalar potential respectively.
Obtain Maxwell's wave equations satisfied by the scalar and vector potentials in the absence of charge an4 current. ·
10
Q.8(a) Derive an expression for the Fermi energy for a free electron gas at T 0. Compute the Fermi temperature of Cu Jssuming the density 9 gms/cm3 and one conduction electron
Q. The figure below represents an imaginary ideal gas cycle. Assuming constant heat capacities,
show that the thermal efficiency is
<img src='./qimages/1297-8a.jpg' 15
Q. A parallel plate capacitor is connected to a battery. What is the electric current while the
capacitor is being charged What is the displacement current between the plates of the capacitor Show that the rate of increase of the electric energy is equal to the surface
integral, of the Poynting vector over the surface enclosing the volume between the plates of the capacitor. 20
<img src='./qimages/1297-8c.jpg'
jC-HENT-N-YPNMAj
PHYSICS
ITime Allowed Three Hours I IMaximum Marks 20Q I
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 Sare compulsory. Out of the remaining SIX questions, THREE are to be attempted I
selecting at least ONE question from each of the two Sections A and B.
All questions carry equal marks. The number of marks carried by a part of a question 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.
All parts and sub-parts of a question are to be attempted together in the answer book.
Any page .or portion of the page left blank in the Answer Book must be clearly struck out.
Useful Constants
Electron charge 1.602 x 10-19 C
Electron rest mass 9.109 X 10-JI kg
Proton mass 1.672 X 10-:27 kg
p
Vacuum permittivity 8.854 x 10-12 farad/m
Vacuum permeability l.257 x 10-6 henry/m
Velocity of light in free space 3 x 108 mis
Boltzmann constant 1.38 x 10-23 J/K
Electron volt J.602 X 10-19 J
Planck's constant 6.62 X 1 o-J4 J-S
Stefan's constant 5.67 x 10-s wm-2 K-4
Avogadro's number 6.02 x 1026 kmol-1
Gas constant 8.31 x 103 J kmot-1 K-1
exp 2.7183
C-HENT-N-YPNMA
000
SECTION-A
Q. 1. Answer the following
8X5=40
Q. Using the concept ofD'Alembert's principle, show that the generalized force can be defined as <img src='./qimages/1297-1a.jpg'> where ri is the Cartesiflll coordinate of the ith particle experiencing external force Fi and qj stands for the generalized coordinate. Discuss the significance of the above expression.
Q. Write down the mathematical representation of Fermat's principle and explain all the notations used.
With the help of a neJt diagram, show that this principle can be used to· obtain the law of refraction
n1 sino1=n2 sin02.
where n1 and n2 are th.. refractive indices of the two media while 8and 82 are the angles of incidence and refrabtion of the light.beam. 8
Q. If the system matrix for a thin lens of focal length f is given by
o
show that the system rpatrix for a combination of two thin lenses of focal lengths fand f2 separated by a distance d can be obtained as
<img src='./qimages/1297-1c.jpg'>
Q.l(d) A left circularly polarized beam 5893°A) is incident normally on a calcite crystal (with its optic axis cut parallel to the surface) of thickness 0.005141 mm. What will be the state of polarizaticln of the emergent beam Ju..tify your answer. Here the refractive indices for t..e ordinacy and the extraordinary rays are l.65836 and 1.48641 respectively.
Q. Deduce the minimum.lnergy.of a·gamma ray photon (in which can cause electro: positron pair production. 8
Q. State Hamilton's principle for a system of particles. If I and L represent the action integral and the Lagrangian furiction,·respectively, write down.the mathematical form ofHainilton's principle and explain /clearly the significance of the same. 15
Q. Discuss the torque-free motion of a symmetric rigid body and hence estimate the period of precession of Earth's polar axis. [Use i3-i1/i3 =0.33, where i1, i2 and i3 are the moments of inertia about the 1Le principal axes the Earth] 15
Q. A particle o..rest mass M moving at a velocity u cQllides with a stationary particle of rest ·
mass m. If the particles stick together, show that the speed of the composite ball is equal
<img src='./qimages/1297-2c.jpg'>
Q. Derive the law of addition of relativistic velocities. Us_e it to prove that under the Lorentz
transformation no two velocities can add upto more. than tbe value of the speed of iight. 15
Q. Starting with the rate equations for matter-radiation interaction, show that the ·ratio of the Einstein's A and B coefficients is proportional. to the third power of the frequency of radiation. 15
Q. How does the population inversion in an active medium lead to the amplification of light .in a laser Explain in details.
Q. Explain how you can construct a zone plate from Fresnel's half perfod zone. Show that a zone plate has multiple foci. 15 .
·Q. What are the step index andgraded index optical ·fibers · · What ·are the conventional optical windows for light propagation through optical fibers l 5
Q. Draw a neat diagram to show how light propagates through a graded index optical fiber ·
from the entrance to the fiber end and explain. 10
SECTION-8
Q. 5. Answer the following
8XS=40
Q. Prove Stefan'.. law of radiation from thennodyn..ic considerations. 8
Q. For a degenerate Fermi-Di_rac gas. the concentration of nucleons .in nuclear matter is N 1.1 x 1038 cm-3• Calculate the· Fermienergy and Fermi temperature.. 8
Q. Suppose a cavity of vol..me V contains biackbody radiation in equilibrium with the walls of the cavity at a temperature T. For a reversible adiabatic change of volume show that VT3 constant. If the initial temperature is 2000°K and the volume is incre_ased-fro.. _10 cm3 to 1250 c m3, reversibly and adiabatically, what would be the final temperature of the radiation 8
Q. Compute the electrostatic energy of a conducting solid sphere of radius R and having the total charge q using the expression for the electrostatic energy in terms of the electric field e of the above sphere.
Q.5(e) Show that the elemental !quantity of heat dQ is not a total differential.field E of the above sphere. 8
Q.6(a) Explain Kirchoff's circuit laws. Using Kirchooffs laws find currents I1, I2 and I3 in the
circuit shown below for R1= 100 R2 200 omegha R3= 300omegha E1= 3 E2= 4 V.
<img src='./qimages/1297-6a.jpg'>
q.6(b).An inductance capacitance C and resistance Rare connected iwith AC source driving Jith Erms 120 V at
f=60 Hz. Compute the power factor and
average power dissipated;in the resistance if R 200 XL 80 Q and Xc= 150omegha.
Q A sphere of homogeneous linear dielectric material is placed in an otherwise uniform electric field E0 Find th.. electric field inside the sphere. 15
Q. A plane electromagnetic +ave of frequency w1 travelling in z-direction and polarized in
x-direction is incident on ·a dielectric medium separatecl by a plane boundary in the x-z
plane. Show that the tranfmission and reflection coefficient are given by
<img src='./qimages/1297-7a.jpg'
where n1 and n2 are the refractive indices of the first a,nd the second medium. 20
Write Maxwell's equations in the absence of a medium.
Explain the gauge transformation and gauge invariance. Show that the relation
div A +1/cdelta0/deltat is Lorentz-covariant, where A and are the vector potential and the scalar potential respectively.
Obtain Maxwell's wave equations satisfied by the scalar and vector potentials in the absence of charge an4 current. ·
10
Q.8(a) Derive an expression for the Fermi energy for a free electron gas at T 0. Compute the Fermi temperature of Cu Jssuming the density 9 gms/cm3 and one conduction electron
Q. The figure below represents an imaginary ideal gas cycle. Assuming constant heat capacities,
show that the thermal efficiency is
<img src='./qimages/1297-8a.jpg' 15
Q. A parallel plate capacitor is connected to a battery. What is the electric current while the
capacitor is being charged What is the displacement current between the plates of the capacitor Show that the rate of increase of the electric energy is equal to the surface
integral, of the Poynting vector over the surface enclosing the volume between the plates of the capacitor. 20
<img src='./qimages/1297-8c.jpg'