Audiencias de proceso debido

This paper consists of twelve questions only. Attempt All questions.

Marks for questions are shown in the right hand margin. Use of Calculator is NOT PERMITTED.

Useful Data :

Planck's constant

h

6.63x10"34J-s

Boltzmann's constant

k

1.38x10"23J/K Charge of an electron

e =

1.6X10"19C Universal gas constant

R

8.314 Jmol"1 K'1

Wien's constant

b

0.29 cm K.

Permeability of free space M-o = 4tc x 10"7 H/m

Permittivity of free space E0 = 8.8 x 10"12 F/m Acceleration due to gravity g = 10m/s2

Gravitational Constant

G

6.67 x10"1 1 Nm2 /kg

RSM-12-P-l-IV-T(M)-PH-2

1. An ice cube of mass 0.1 Kg at 0°C is placed in an isolated container which is at 227°C. The specific heat S of the container varies with temperature T according to the empirical relation S = A+BT, where A = 100cal/Kg-K and B = 2 x 10~2cal/Kg-K2. If the final temperature of the container is 27°C, determine the mass of the container.

[ 5 ]

2. An ideal massless spring can be compressed 1 m by a force of 100 N. The same spring is placed at the bottom of a frictionless inclined plane which makes an angle 9 = 30° with the horizontal. A 10 kg mass is released from rest at the top of the incline and is brought to rest momentarily after compressing the spring 2 meters.

(a) Through what distance does the mass slide before coming to rest ?

(b) What is the speed of the mass just before it reaches the spring ? [10] 3. A circular loop of radius R is bent along a

diameter and given a shape as shown in the figure. One of the semicircles (KNM) lies in the x- z plane and the other one (KLM) in the y-z plane with their centres at the origin. Current I is flowing through each of the semicircles as shown in figure.

(a) A particle of charge q is released at the origin with a velocity v = - v0i . Find the instantaneous force f on the particle. Assume that space is gravity free.

(b) If an external uniform magnetic field B j is applied determined the forces F.) and F2 on the semicircles KLM and KNM due to this field and the net force F on the loop.

4. A thin uniform metallic rod of length 0.5 m and radius 0.1cm rotates with an angular velocity 400 radian/second in horizontal plane about a vertical axis passing through one of its ends. Calculate the tension in the rod and elongation of the rod. The density of the material of the rod is 104 kg/m3 and Young's modulus is 2 x 1011 N/m2.

[ 5 ]

5. (a) We know that velocity of a wave travelling along a stretched string is given by VT/V where T is the tension in the string and (i is the mass per unit length of the string. Find the time taken by the wave travelling along a vertically suspended string

of mass'm' and lengthT from the free end to the fixed end. [5] (b) A band playing music at a frequency f is moving towards a wall at a speed vb . A

motorist is following the band with a speed vm. If v is the speed of sound, obtain an

expression for the beat frequency heard by the motorist. [5] 6. A plank of mass M rests on a smooth horizontal plane. A sphere of mass m is placed on the

rough upper surface of the plank and the plank is suddenly given a velocity v in the direction of its length. Find the time after which the sphere begins pure rolling, if the coefficient of

friction between the plank and the sphere is \i and the plank is sufficiently long. [10] 7. A f.i-meson particle moves in a circular orbit around a very heavy nucleus (of infinite

mass) of charge + 3e. Assuming Bohr's model is applicable to this system, (a) derive an expression for the radius of nth Bohr orbit.

RSM-12-P-l-IV-T(M)-PH-3

(b) find n for which radius of orbit is approximately same as that of 1st Bohr orbit for a hydrogen atom.

(c) find wavelength of radiation emitted when ji.- meson jumps from 3rd orbit to Ist orbit - meson is a particle, whose charge = that of an electron, mass = 208 times

that of an electron], [10] 8. A rocket is fired vertically and ascends with constant vertical acceleration of 20m/s2 for

1 minute. Its fuel is then all used and it continues as a free particle. Find the (a) maximum height reached by the rocket.

(b) total time elapsed from the take off till the rocket strikes the earth.(g=10m/s2) [10] 9. Consider two small balls connected to a rigid rod

of length '21' which in turn is suspended by a thread & rotated about the thread at angular velocity co. What would be the magnitude & direction of total force exerted by rod on one of the balls?

[10] 10. Find an expression for the magnetic dipole moment and magnetic field induction at the center of a Bohr's hypothetical hydrogen atom in the nth orbit of the electron in

terms of universal constants . [5] 11. An inductor of inductance L = 400 mH and resisters

of resistances Ri = 2Q and R2 -2C1 are connected to a battery of e.m.f. E = 12V as shown in the figure. The internal resistance of the battery is negligible. The switch S is closed at time t = 0. What is the potential drop across L as a function of time? After the steady state is reached, the switch is opened. What is the direction and magnitude of current through F^ as a function of time?

Ri-

[5]

12. A point source is placed at a distance d/2 below the principal axis of an equiconvex lens of refractive

3

index — and radius 20-cm. The emergent light from lens fall on the slits ST and s2 placed symmetrically

with the principal axis. The resulting interference & pattern is observed on the screen kept at a distance s

D = 1 m from the slit plane. Find V (a) the position of central maxima and its width

(b) the intensity at point O [5+5=10]

SI

In document Arizona Center for Disability Law. Organismo de Protección y Abogacía de Arizona (página 124-131)