PHE-5 : MATHEMATICAL METHODS IN PHYSICS-II Instructions : 7. Students registered for both PHE-4 & PHE-5 courses

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1 No. of Printed Pages : (.0 BACHELOR OF SCIENCE (B.Sc.) Term-End Examination June, 2010 PHYSICS PHE- I PHE- : MATHEMATICAL METHODS IN PHYSICS-I Time : 1 1/2 hours Maximum Marks : 25 B.Sc. EXAMINATION, PHE- : MATHEMATICAL METHODS IN PHYSICS-I PHE-5 : MATHEMATICAL METHODS IN PHYSICS-II Instructions : 7. Students registered for both PHE- & PHE-5 courses should answer both the question papers in two separate answer books entering their enrolment number, course code and course title clearly on both the answer books. 2. Students who have registered for PHE- or PHE-5 should answer the relevant question paper after entering their enrolment number, course code and course title on the answer book. Note : Attempt all questions. The marks for each question are indicated against it. Symbols have their usual meanings. You may use log tables or a calculator. PHE- 1 P.T.O.

2 1. Attempt any three parts : x3=12 For two vectors A and B, if A + BHA B 1, find the angle between A -3 and B. Show that the derivative of vector function (t) of constant magnitude is either the null vector or is perpendicular to it. Show that the following vector field is irrotational : --> ---> K r F r 2 Define polar and axial vectors show that axial vectors do not change sign under a parity transformation. (e) Using Gauss's divergence theorem, evaluate F.d S over a spherical surface of A A radius R where F=x 3 i+y3 j + z3 k. 2. The position vector of a particle is given by -- A A r (t) = 5t ep + sin t ez Calculate its acceleration. OR Determine the work done by a force field F in moving particle once around a circle C in the x y plane if the centre of the circle is at the origin and its radius is 3, where F is given by 5 5 F = (2 x y)1+ (x + y)i PHE- 2

3 A factory manufactures watches. The probability of a watch being defective is If 0 watches are selected at random, what is the probability that no more than three are defective? OR Three coins are tossed in a game. Let E be the event that a tail appears on the first coin and F be the event that a head appears on the third throw. Are E and F independent? Obtain the expression for the standard deviation of the poisson distribution. OR From the center of steel bar, supported at its ends, a mass M is suspended. The depressions y (um) is measured for various masses as follows : M (kg) y (p,m) Calculate the best value of the slope PHE- 3 P.T.O.

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6 ^Iri FART 7' WIT xy ti licio fp-ta- 5 i ct.) WI{ 'FAA rck 717 chitiw TITff Wff l fqg I 1171 c t-q fg tr-{ t h 31:1 f r 3 t; 1 --t tin t : F = (2 x y) + (x+y)// 7-* chltts0 13rNt 19-0T t tg t Niiti chrit 0.02 t I gli-crt9tif 1.11'1 t-9. \rtitc( stit (sum 3 t Ntiti choi AzIT t? alardt ari 1*i rti c Wit W- t 1 7ft, E *-crg t F dom Fqx-i t ca:ere atukqcii t? teir:11 tsidq * -111) R1101 eqqi ch NTEI 'et I 3TMT 317 WtR atrof--a.crrut qoil-111 M odchi g i Trzir t fit- f rzima- TR y (pm) Fig ci t : M (kg) y (p,m) ci I cll i kid1 1 TIN 3TET I PHE- 7 P.T.O.