Physics - Main Examination -
2002
Time allowed: Three hours
Maximum marks: 300
Instructions
(more content follows the advertisement below) A D V E R T I S E M E N T
Each question is printed both
in Hindi and in English.
Answers must be written in the
medium specified in the Admission Certificate issued to you, which must be
stated clearly on the cover of the answer book in the space provided for the
purpose. No marks will be given for the answers written in a medium other than
that specified in the Admission Certificate.
Candidates should attempt
Questions 1 and 5 which are compulsory, and any three of the remaining questions
selecting at least one question from each section.
Assume suitable data if
considered necessary and indicate the same clearly.
All questions carry equal
marks.
PAPER I
SECTION A.
1. Answer any three of the
following:
(a) Using the rocket equation
and its integral find the final velocity of a single stage rocket. Given that (i)
the velocity of the escaping gas is 2500 m/s, (ii) the rate of loss of mass is.
(where m0) is the initial mass and 0.27 m0 is the final
mass).
(b) Two spaceships are moving
at a velocity of 0.9 c relative to the Earth in opposite directions. What is the
speed of one spaceship relative to the other? (c = velocity of light)
(c) A wave is represented by - Find wavelength
, velocity v, frequency f and the direction of propagation. If it interferes
with another was given
, find the amplitude and the phase of the resultant
wave (All dimensions are in SI system).
(d) Derive the expression for resolving power of a diffraction grating with N
lines. Calculate the minimum number of lines in the diffraction grating if it
has to resolve the yellow lines of sodium (589.0 nm and 589.6 nm) in the first
order.
2. (a) Using the Lagrangian for the system of a planet and the Sun obtain the
equation of motion. Use them to get the equations for the orbit.
2. (b) Derive the relationship between the impact parameter and the scattering
angle for the scattering of an particle of charge +2e by a nucleus of charge +Ze.
Calculate the impact parameter for an angle of deflection of 30o if
the kinetic energy of the alpha particle is 6x10-13 J.
3. (a) State Fermat's principle. Apply it to get the laws of reflection from a
plane surface.
3. (b) The phase velocity of the surface wave in a liquid of
surface tension T and density is given by
. Show that the group velocity vg
of the surface wave is given by
3. (c) An observer A sees two events at the same space point ()
and separated in time by t=10-6 s.
Another observer B sees them to be separated t' = 3x10-6 s. What is
the separation in space of the tow events as observed by B? What is the speed of
B relative to A?
4. (a) How do you know that the light is a transverse wave? What is a quarter
wave plate? How is it constructed?
4. (b) Discuss the Fresnel diffraction pattern formed by a straight edge using
the Cornu's spiral.
4. (c) In an experiment using a Michelson interferometer, explain with the help
of suitable ray diagrams
(i) Why do we need extended source of light,
(ii) Why do we get circular fringes, and
(iii) Shifting of fringes inwards or outwards as we shift the movable mirror.
SECTION B
5. Solve any three of the following:
5. (a). Calculate the electric field for a point on the axis of a uniform ring
of a charge 'q' and radis a. Where does the maximum value occur.
5. (b) Show that the potential energy of a charge Q uniformly distributed
throughout the sphere of radius R is give by .
5. (c) Describe Carnot cycle and show that efficiency is given by
, where the symbols have their
usual meaning.
5. (d) Derive the Bose-Einsten distribution for an ideal gas.
6. (a) Using Kirchoff's laws find currents in each branch of the circuit shown
in the following diagram.
6. (b) A Geiger tube consists
of a wire a wire of radius 0.2 mm and length 12 cm and a co-axial metallic
cylinder of radius 1.5 cm and length 12 cm. Find
(i) the capacitance of the
system, and
(ii) the charge per unit length
of the wire when the potential difference between the wire and the cylinder is
1.2 kV.
6. (c) A series LCR circuit
with L = 2 H, C = 2 F and R = 20 ohm is powered by a source of 100 volts and
variable frequency. Find
(i) the resonance frequency, fo,
(ii) the value of Q
(iii) the width of resonance f
and
(iv) the maximum current at
resonance.
7. (a) Why did Maxwell have to
introduce the idea of displacement current? Derive the wave equation from
Maxwell's laws. Obtain Fresnel's formula for reflection and transmission
coefficients of the electric vector when it is perpendicular to the plane of
incidence.
7. (b) What are vector and
scalar potentials for the electromagnetic field? Are they unique? Explain what
are Coulomb's and Lorentz gauges. Derive the electromagnetic wave equation in
Lorentz gauge and show that it is equivalent to Maxwell's equation.
8. (a) Discuss the phenomenon
of Bose-Einstein condensation. Obtain the expression for the condensation
temperature. Briefly comment on observation of Bose-Einstein condensate.
8. (b) A bulb filament is
constructed from a tungsten wire of length 2 cm and diameter 50
m. It is enclosed in a vacuum bulb. What temperature does it reach when it is
operated at a power of 1 watt? Given:
(i) Emissivity of tungsten = 0.4
(ii) Stefan's constant = 5.67x10-8 watt/m2K4.
Paper II
Instructions
Each question is printed both
in Hindi and in English.
Answers must be written in the
medium specified in the Admission Certificate issued to you, which must be
stated clearly on the cover of the answer book in the space provided for the
purpose. No marks will be given for the answers written in a medium other than
that specified in the Admission Certificate.
Candidates should attempt
Questions 1 and 5 which are compulsory, and any three of the
remaining questions selecting at least one question from each section.
Assume suitable data if
considered necessary and indicate the same clearly. Some constants are given
below.
All questions carry equal
marks.
1. Answer
any three of the following:
1. (a) (i)
The wave function of a particle is . Find the expectation values of position (x)
and momentum (p) for the particle (10)
1. (a) (ii)
A 200 eV increase in the energy of an electron changes its De Broglie wavelength
by a factor of two. Calculate the initial De Broglie wavelength of the
electron.
1. (b). (i)
What is the lowest non zero angular momentum for an elementary particle? Name at
least three elementary particles having such an angular momentum (10)
1. (b) (ii)
Write the spectral symbol of the term with S= 1/2, J = 5/2 and g = 6/7. (10)
1. (c) (i) A
sample is irradiated by a 5000 A radiation to give a Raman line at 5050.5 A.
Calculate the Raman frequency.
1. (c) (ii)
Explain, both red and violet degraded bands have been observed in electronic
band systems, but rotation-vibration spectra show bands degraded to red only.
(10)
1. (d) (i)
Treating CH molecule as an united atom, derive its resultant molecular
electronic states. (10)
1. (d) (ii)
Calculate the moment of inertia of HCl molecule from the expression =
20.68 (J+1), where J=0,1,2,... (10)
2. (a) Solve
the one dimensional Schrodinger wave equation with potential:
V(x) = 0 for x<-a
V(x) = V0 for -a <x <a
V(x) = 0 for x >a
2. (b)
Distinguish between a classical and a quantum mechanical harmonic oscillator.
Explain the existence of zero point energy. (15)
2. (c). Show
that the motion of a classical particle is analogous to the motion of a wave
packet, which can be constructed by superposition of a large number of plane
waves. Construct such a wave packet and derive an expression for its group
velocity. (25)
3. (a)
Derive an expression for the spin-orbit interaction energy in one electro
system. Calculate the energy separation between the levels 2P1/2
and 2P3/2. (20).
3. (b).
Write the electronic configuration of mercury (Z = 80). Obtain the spectral term
for the normal and the first excited configuration of the atom (20).
3. (c).
Derive an expression for the electrical conductivity of metals on the basis of
free electron theory of metals. (20)
4. (a) A
diatomic gas is found to have a number of absorption bands in the ultraviolet
region. Each band is also observed to have a fine structure. How can the
observed spectrum be explained and analyzed? (25)
4. (b)
Explain the nature, origin and significance of 21 cm hydrogen line. (20)
4. (c)
Calculate the change in rotational constant (Bv) when deuterium is
substituted for hydrogen in a hydrogen molecule. (15).
Section B
5. Answer
any three of the following.
5. (a) (i)
Explain why a neutral particle such as neutron possesses a finite value of
magnetic moment, and how it is determined. (10).
5. (a) (ii)
Write down the electronic configuration of 7Li, 13C, ad
25Mg in the ground state of the nuclear shell model. (10)
5. (b) (i)
Explain how neutrino was discovered from the -decay of radioactive nuclei. (10)
5. (b) (ii)
Show that for a cubic lattice, the difference between the successive h, k, l
planes is given by . (10).
5. (c) (i)
Discuss the variation of free carrier concentration with temperature for an
intrinsic and extrinsic semiconductors. (12).
5. (c) (ii)
Explain the effect of negative and positive voltage feedback on an amplifier
characteristics. (8)
5. (d) (i)
Show that a negative logic OR gate is like a positive logic AND gate. (10).
5. (d) (ii)
Distinguish between Hadrons and Leptons. (10)
6. (a) Which
conservation laws are obeyed in nuclear reactions? Explain the significance of Q
value of a nuclear reaction. (30).
6. (b)
Explain shell model of the nucleus. Give evidence for nuclear shell structure.
What are the limitations of the shell model? (30)
7. (a)
Explain Meissner effect and Josephson effect. Describe their applications in
the field of superconductivity. (20)
7. (b)
Distinguish between particle and antiparticle. How antiparticles were
discovered? (20)
7. (c)
Mention the conservation laws for strong, electromagnetic, and weak
interactions. (20).
8. (a) What
are the main applications of JFET? Discuss their advantages over bipolar
transistors. Explain the working of n-channel JFET with the help of a schematic
diagram. (30)
8. (b) Write
down the characteristics of an ideal operational amplifier. Explain the term
virtual ground. Draw a circuit diagram showing virtual ground in an operational
amplifier. (30)
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