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ET-105(A)o. of Printed Pages : 6B.Tech. Civil (Construction Management) /B.Tech. Civil (Water Resources Engineering)

Term-End Exam inationET-105(A) : PHY SICS 04324

Time : 3 hoursaximum Marks : 70Note : All questions are compulsory. Symbols have their usualmeanings. Use of calculator is permitted.

1.ttempt any five of the following :x4=20(a) The distance of Mars from the Earth is

0.52 AU while that of Jupiter is 4.2 AU. Ifthe orbital period of Mars is 1.88 years, findthe orbital period of Jupiter.1AU ( a 1.5 x 101 1 m) is the distance of theearth from the sun.

(b) A proton has a velocity of 4 x 104 i m/s. Itenters an electric field

AE= 835 i +1670 j N/C. How far does theproton move in the x direction before itcomes to a stop ? At that instant how farhas it travelled in the y direction ?(c) Find the moment of inertia of solid sphereof uniform density about any diameter andany tangent to its surface.

June, 2011

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(d) The index of refraction of a substance isfound to vary inversely as the wavelengthin vacuum. Show that the group velocity ishalf the phase velocity.

(e) A 60 W bulb radiates energy equally in allthe directions. Calculate the amplitude ofthe electric and magnetic fields at a distanceof 1m from the bulb.

(f) A solenoid of length 10 cm has 400 turns. Itsarea of cross-section is 6 cm 2 . Calculate thew ork done in establishing a current of 200 mAin the solenoid. W hat is the energy density inthe interior volume of the solenoid ?

(g) A thin metallic shell of radius R carries acharge Q. At its centre is another pointcharge Q. Find the electric fields atdistances of 2R and R/2 from the centre ofthe shell.

(h) A 12 V battery runs the follow ing circuit. Ifa current of 1.2 A is desired in the arm A B,find the resistance R if the key is open.A 3f212V

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2. Attempt any tw o of the follow ing :x5=10(a) Explain the concept of free body diagram.

A mass m is released from the top of asmooth vertical track of radius R withnegligible speed. Show that if leaves contactwith the track at an angle 0= cos-1(2/3).

(b) State and prove the W ork-Energy Theorem.Using this theorem calculate the speed ofthe bob of a simple pendulum w hen the bobis passing through the equilibrium position.(c) In a scattering process involving a chargedparticle and a stationary nucleus, calculatethe closest distance of approach. If thecharged particle is 5 M eV a particle and thetarget nucleus is gold (z = 79), find theclosest distance of approach.

3. Attempt any two of the follow ing :x5=10(a) Explain the physical significance of moment

of inertia. Establish the theorem ofperpendicular axes. Find the moment ofinertia of a flat circular disk about anydiameter.

(b) Show that the net external torque on asystem of particles is given by ;" -3

Zo =c X F extState Chasles's theorem and sketch thegeneral displacement of a body.

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(c) Write down the equations of motion of arigid body about the z-axis. A billiard ballof mass m and radius R is hit by a cue at apoint at a distance h above its centre. As aresult the ball acquires a speed v0immediately after the impact. Discuss itssubsequen t m otion w ith special reference toh = 2R/5.

4. Attempt any two of the follow ing :x5=10(a) Discuss the composition of two simple

harmonic motions along the y-axis havingequal frequencies. Explain the phenomenonof beats. Can we hear beats if theirfrequency is 15 Hz ?

(b) Define the intensity of sound waves. Showthat when they propagate in air theirintensity varies inversely as the square of thedistance.

(c) W hat should be the w idth of a slit so that itcan produce a diffraction pattern ? Derivean expression for the positions of secondarymaxima in the diffraction pattern of agrating.

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5.ttempt any two of the following :x5=10(a) What is an electric dipole ? Define its

moment. An electric dipole is placed in auniform electric field such that the dipolemoment makes an angle 0 with the electricfield. Show that the configuration ofminimum energy of the dipole is parallel tothe field.

(b) Define electric potential. How is it relatedto the electric field ? Find the potential dueto a line charge carrying charge X per unitlength. Why do you have to fix the constantof integration at a finite distance from theline charge.

(c) In the following circuit find the conditionfor zero current through the branch AB.A fully charged capacitor is allowed todischarge through a resistor. Find anexpression for the flow of current in thecircuit.

A

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6. Attempt any two of the following :x5=10(a) Discuss the significance of the relations

-4 04V B =u and V E =P/0.omputemagnetic induction due to a straight currentalong the z-axis and verify that themagnetic induction satisfies the relation

-,V B =0.(b) A charged particle is projected in a plane

perpendicular to a uniform field of magneticinduction }3 . Discuss and sketch itssubsequent motion. A dentron and ana-particle describe circular orbits of thesame radius in a plane normal to a uniformmagnetic field. What is the ratio of thedentron speed to the a-particle speed ?(c) Explain the need to introduce displacementcurrent in Maxwell's equations. Writedown the equations modified by it. Derivewave equation in free space for the electricfield.Constants :

147r0 = 9 .0 x 109 Nm2 C-21 1 0 = 47 x 10 - 7 Hm-1Mass of a-particle = 6.4 x 10-27 kgMass of a proton =1.67 x 10-27 kgCharge of proton =1.6 x 10-19 C

g =9.8 m/s2.

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