cs (mlAIN) EAAM, 2010
No. 267 e-DTN-K-QZA
PHYSICS
Paper I
ITime Al.1oW"ed Three Hours I IMaxirnuITl Marks 300 I

INSTRUCTIONS
Each question is printed both in Hindi and
in English. AnsUJers must be written in the tnediurn specified in the Admission Certificate issued
to you, UJhich must be stated clearly on the cover of the ansUJer-book in the space provided for the purpose. No marks will be given for the ansUJers Ulritten in a medium other than that specified in the Admission
Certificate.
.
Candidates should attempt Question Nos. and 5 UJhich are and any three of the rem.aining questions selecting at least one question from each Section.
The number of marks carried by each question is indicated at the end of the question.
Assume suitable data if considered necessary and indicate the same clearly. SymboLS/notations carry their Usual
..
unless othenuise indicated.
Section-A
1. AnsWer all the six below: IOx6=60
A uniform solid sphere of radius R having rnOITlent of inertia I about its diameter is melted to form a uniform disc of thickness t and radius r. The InOITlent of inertia of the disc about an axis passing through its edge and perpendicular to the plane is also equal to I. Sho'W that the radius r of· the disc .. b 2R
IS gIven
Two thin symmetrical lenses of two different natures (convex and concave) and of different materials have equal radii of curvature R =15 ern. The lenses are put close together and immersed in water (J...l tv 4 3). The focal length of the system in water is 30 ern. Show that the difference between the refractive indices of turo lenses is 1/3.
(c)What is the significance of the null result of Michelson-Morley experiDlent? Does it disprove the existence of ether? Justify.
optical beam of spectral width 7·5 GHz at wavelength A 600 nm is incident normally on Fabry-Perot etalon of thickness 100 InIn. Taking refractive index unio/, find the nUlDber of axial modes 'Which can be supported by the etalon.

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An un polarized light beaTIl of intensity 1000 W 1m 2 is incident on an ideal linear polarizer "With its transITlission axis parallel to vertical direction. Describe an experiment to reduce the intensity of light beaIn to 500 W /Ul2 .
What should be the refractive index of cladding of an optical fibre with nUlTlerical aperture 0·5 with refractive index of core as 1·5?
. What are Eulerian angles? A body with rotational symmetry about an axis is rotating under gravity about a point on the axis v without friction. What are the quantities remaining constant during the nlotion? Find then tn in terms of suitable Eulerian angles. Explain 4'precession7 and €nutationJl of such a body. 25
A planet revolves around the Sun in an elliptic orbit of eccentricity e. If T is the tilTIe period of the planet, find the time spent by the planet between the ends of the minor axis close to the Sun. 10 When a sphere of radius r falls down a homogeneous viscous fluid of -unliIll.ited extent with the tenninal velocity the retarding viscous force acting on the sphere depends on the coefficient of viscosity TJ, the radius r and its velocity v. ShoW" how Stokes' la'W 'Vas arrived a t connecting these quantities froIn. the dimensional considerations. 10
In the propagation of longitudinal waves in a fluid contained in an infinitely long tUQe of cross-section show that p where, Po equilibriuIn density p density of the fluid in the disturbed state voluIne strain I« 15
3. If a photon of frequency v collides with an electron of lTlass 1Tlo at rest, it lNill be scattered at SOIne angle e 'With a new frequency Show that the change in wavelength is related to the scattering angle by the forII1ula AI A 2Ac Where AC hmoc IS knOW'll as the Compton "Wavelength. 20 ShoW" that two convex lenses of the same material kept separated by a distance a., "Which is equal to the average of tv.ro focal lengths, Inay be used as an 1achroITlat, that is, a -lfl f 2).2 10
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Describe Michelson interferometer for evaluation of coherence length of an optical beam.. Calculate coherence length of a light beaIn of wavelength 600 nm with spectral "Width of 0·0 1 nm.
20+10
4. Obtain the expression for the primary focal length of Fresnel zone plate. 20
Show that two light beams polarized in perpendicular directions will not interfere. 15
laser beam of 1microIneter wavelength with 3 megawatts power of beam diameter 10 ITlrn is focussed by a lens of focal length 50 mIn. Evaluate the electric field associated Mth the light beam at the focal point.
(Dielectric permittivity of free space, eo 8·8542 X 10-12 C 2 25
Section-B
5. Ans'Wer all the six below lOx6=60
(a)Obtain Poissons equation In electrostatics from Gauss' laW. What form does it take 'When the charge density is zero?
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A wire of length 2m. is perpendicular to X-y plane. It is It loved with a velocity
V i bar 3j bar k bar) m8-1 through a region
of unifolTIl'induction B bar 2j bar) W . COITlpute the potential difference between the ends of the 'Wire.
What happens if the priInary finding of a transformer is connected to a battery?
1 kInol of an ideal gas is cOIll.pressed isothermally at 400 K froIn. 100 kPa to 1000 kPa in a piston and cylinder arrangelTlent. Calculate the entropy change of the gas, the entropy change of the surroundings and the total entropy change resulting from the process if the process is :mechanically reversible and the surroundings consist of a heat reservoir at 400 K.
Calculate the change in pressure for a change in freezing point of water equal to -0·91 °C. Given, the increase of specific volume -when 1 grn of water freezes into ice is 0-091 cc/gm and latent heat of fusion of ice is 80 callgIn.
(f) Calculate the nUITlber of different arrangements of 10 indistinguishable particles in 15 cells of equal a priori probability, considering that one cell contains only one particle.
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what is meant by a dielectric? define polarization vector p and relate it with the average molecular dipole moment. obtain expression for the potential due to a polarized dielectric in terms of the polarization vector.
discuss the growth of current when an e.m.f. is suddenly applied to a circuit containing resistance, induction and capacitance in series. what is the time constant of the circuit?
a series circuit has an inductance of 200 microhenries, a capacitance of 0.0005 microhenries, a capacitance of 0.0005 microfarad and a resistance of 10 ohms. find the resonanat frequency and quality factor of the circuit.
using maxwells field equations for a homogeneous non-conducting medium,derive the wave equations for the electric field. calculate the velocity of em wave in free space.
(b).explain the term poynting vector and state the significance of poynting theorem.
calculate the skin depth for radio waves in free space of wavelength 3m in copper, given that electrical conductivity for copper is 6into107 omega1 m1
8. Consider one mole of an ideal gas 'Whose pressure changes with volume as P ex.V p where a is a constant. ,If it is expanded such that its volume increases m titnes, find the change in internal energy, work done by the gas and heat capacity of the gas. 25
Derive an expression for the thennal efficiency of a reversible heat engine operating on the Diesel cycle with an ideal gas of constant heat capacity as the working ITlediull1.. 25
Consider the following stateIrlent 'vrhe Fenni energy of a given material is the energy of that quantulTI state "Which has the probability equal to of being occupied by the conduction electrons." Is the above statement correct? Give reasons for your anS'Ver.

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