Stefan's constant a = 5.67 x 10~8 Jm~2 sec"1 K*
Name of the candidate
Enrollment Number
AITS-2002-FT-IV-PH-2
1. A man is standing on a high cliff and he drops a sonic device (at t = 0) of mass 5.4 kg from there. It is found that the air resistance is equal to kv; where k = 1.7 and v is the instantaneous velocity of the body. The sonic device emits frequency of 700 Hz. The man hears a frequency of 660 Hz after some time. What was the speed of device and time when it has emitted the note corresponding to this frequency. Also find the minimum frequency heard by the man.
(Given, natural logarithimic exponent e = 2.7 and velocity of sound = 330 m/s) [10] The P-T curve of a cyclic process undergone by one mole of a
monatomic gas is as shown.
The process AB is given by equation P = aT1/2.
(a) Find work done and heat exchange in each process. (b) Also, find the molar specific heat of the gas for process AB.
4T0 T
[8+2=10] 2£
AB. BC and CA are identical rods of length forming a V3
triangular frame (A, B, C are joints) kept on a smooth horizontal table. A particle of mass m and velocity 2v0 normally hits the rod BC as shown in the figure. The particle collides elastically and come to rest immediately after the collision. (Assume that the particle is immediately removed after the collision).
[4+3+3=10] (a) Find ratio —; where M = mass of each rod, m = mass of incident particle.
M
(b) Find velocity of vertex A immediately after impact.
(c) Find the time after which the frame regains its original orientation for first time after impact and the distance moved by 'O' (Centroid of the AABC) in that time.
A block of mass m is attached to one end of a long elastic rope. The other end of the elastic rope is fixed to the roof of a building. Initially the block is in contact with the roof at the point where the rope is fixed and is allowed to fall freely from rest. The unstretched length of the rope is L and has a force constant k.
(i) If the block just reaches the floor find the height of the room. (ii) what is the maximum speed of the block during this drop.
(iii) The time taken during the drop before coming to rest for first time.
(Take acceleration due to gravity as g) [3+3+5=11] An open cylinder is rigidly fixed to a floor. AB is a piston of mass 9 kg and of cross-sectional
area A = 5n2 x 10"4 m2 (equal to the cross-sectional area of the cylinder). Piston is free to move on smooth inner surface of the cylinder as shown in the figure. Spring of stiffness 7c2N/m is attached to piston and to a rigid wall as shown. It is initially compressed by 1m. The thread which initially holds piston AB at rest snaps at t = 0.
< 2^5m i . A
/rmwr t
AITS-2002-FT-IV-PH-3
(i) Find the time for all resonances till the spring is at its maximum elongation for first time, if the air column is made to vibrate with a tuning fork of frequency 320 Hz. Velocity of sound = 320 m/s.
(ii) If P0 (N/m2) is the atmospheric pressure present inside and outside the cylinder and AP0 (N/m2) is the maximum amplitude of pressure variation in the air column inside the cylinder then find the maximum pressure on the piston and its position from open end of tube when
this occurs. [6+2=8] A thin convex lens of focal length 30 cm and having aperture diameter d = 1 cm is used to
focus sun rays on a metal surface. The absolute temperature of sun is 6000 K and assume that rays fall on the lens normally. The work function of the metal is 1.48 eV. Assume that sun radiates like a black-body and it radiates a single wavelength corresponding to its maximum spectral radiancy
(a) Find the intensity on the metal surface.
(b) What is the de-Broglie wavelength of the photoelectrons emitted.
(Given Wein's constant = 3 x 10"3 mK). [7+3=10]
7. There are two fixed identical rings A and B of radius a = 3m. Their centres O and O' lie along y axis as shown. Given H = 4 m. Coordinates of O' are (0, 0). Charge on ring A is +q and on B is +nq. A positive charge q0 of mass m is dropped from O and it just reaches O'.
(a) Find the value of n. given m = t'q°
Ay
C
2ne0g
(b) Plot a rough sketch of potential energy of the falling particle as a^unction of its height above O'
In the shown figure PQ is a semi-circular arc of radius r. QR and RP are straight wires and OR = OQ = OP. They form a mesh PQR which is not in a plane. A current I flows through circuit along the direction shown in the figure. A magnetic field B exists in the space such that B is equally inclined with positive direction of all the three axis.
(a) Calculate moment of force (x) acting on the circuit. (b) Now suppose if there is no current in the circuit and the magnitude of magnetic field starts increasing at a constant
dB
= a. Calculate magnitude of emf induced in the
O
3'
3
Brate dt
mesh and show direction of flow of induced current in the mesh.
[6+2=8]
» X
[6+6=12]
(a) A satellite is orbiting the earth in equatorial plane in a circular orbit having radius 2R and same sense of a rotation as that of the earth. Find the duration of time for which a man standing on the equator will be able to see the satellite continuously. Assume that the man
can see the satellite when it is above the horizon. [5] (b) A wooden block (having cross-sectional area A), with a
coin (having volume V and density d) placed on its top, floats in water as shown in figure. If the coin is lifted and then dropped into water, find
(i) change in the submerged length (£) of the block. (ii) change in the water level (h) in container.
Cross sectional area of the container is & density of
water is p. ' [3+3=6] fllTJCC Ltd., ICES House, Sarvapriya Vihar (Near Hauz Khas B. • Term.), New Delhi - 16, Ph : 6515949 . 6865182, 6569493, Fax : 6513942
AITS-2002-FT-IV-PH-4
as jum = The final value of refractive index is found to be The separation
o 10. In a Young's double slit experiment the
region between the slits and the screen is filled with a liquid whose concentration starts changing at t = 0 and because of that its refractive index also changes with time
5 _t_ 2~ 4
5 4
between the slits is d = 2 mm and between the slit and screen is D = 1m. The thickness of glass plate shown in the figure is 36 urn and its refractive index is 1.5.
(a) Find the position of central maxima as a function of time and the time when it is at O.
(b) Find the speed of central maxima when it is at O. [6+4=10]
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