BPHE-101/PHE-01/PHE-02 BACHELOR OF SCIENCE (B.Sc.) Term-End Examination, December, 2015 PHYSICS BPHE-101/PHE-01 : ELEMENTARY MECHANICS

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1 02534 No. of Printed Pages : 15 BPHE-101/PHE-01/PHE-02 BACHELOR OF SCIENCE (B.Sc.) Term-End Examination, December, 2015 PHYSICS BPHE-101/PHE-01 : ELEMENTARY MECHANICS PHE-02 : OSCILLATIONS AND WAVES Instructions : (i) Students registered for both BPHE-101 I PHE-01 and PHE-02 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. (ii) Students who have registered for BPHE-101 I PHE-01 or PHE-02 should answer the relevant question paper after entering their enrolment number, course code and course title on the answer book. *.1:11.7V.t.-101/11/.7V.i.-01/41%7V.t.-02 4t.'.7V.' t-ilict) (A ) TrItfftlft4R, Rti4-alt, :1114W : mlinct) #4 'Acn 111.7w.1.-o2: arf Win (ii) ctayi : 4rfr.civ.e.-101 Itqw.e. -01 ark lit.7w.e " I. IllT4FAWT ri*fff ff, c')-t7 IRTRY drh T drff 3-Piran 1 airr7 ary-a-5-*, Ingeobsi cb?ss upit flly,-twy, ftgwr op/ eult.qw.f.-101 I ult.tg.e rffciv.e.-02 Avit Gki 4-4/Fu. ff, NO. 34 3R 01,1 JR?, 3ff?" VPIW WENT 315M-17*, litqqshit ca5 UP-IT tilq4a5h T fity7-6151) ftwf 1 BPHE-101/PHE-01/PHE P.T.O.

2 BPHE-101/PHE-01 BACHELOR OF SCIENCE (B.Sc.) Term-End Examination December, 2015 BPHE-101/PHE-01 : ELEMENTARY MECHANICS Time : 1 1 hours Maximum Marks : 25 2 Note : Attempt all questions. The marks for each question are indicated against it. Symbols have their usual meanings. You may use log tables or non-programmable calculators. 1. Attempt any two parts : 2x6=12 (a) (i) Is the following statement true or false : "If the instantaneous velocity of an object is zero, its acceleration must also be zero." Explain your answer. 1+1=2 (ii) A block of mass 50 kg is pulled horizontally on a floor. If the coefficient of kinetic friction between the block and the floor is 01, what is the horizontal force required to pull it at a BPHE-101/PHE-01 2 constant velocity? Draw the free-body diagram. 1+1=2

3 (iii) A stone is lodged in a rotating car wheel at a distance of 0.2 m from the axis of rotation. The average angular acceleration of the stone is 100 rad S-2. What will the stone's speed be after 2.0 s? 2 (b) (i) If the free fall acceleration on the moon is measured to be 1.60 ms -2 and its mass is 7.4 x 1022 kg, what is its radius? (G = 6.67 x Nm2 kg-2) 2 (ii) Determine the potential energy function associated with the anharmonic spring force : -> A F = (- kix - k2x2) i. 4 (c) (d) State the work-energy theorem. A fire-cracker of mass 010 kg is launched from rest. The work done on the fire-cracker by non-conservative forces due to burning fuel is 100 J. Calculate the speed of the fire-cracker when it reaches a height of 20 m. Neglect air resistance and the mass lost due to the burning of fuel. Take g = 10 ms2. 2+4=6 A boy of mass 20 kg stands at the edge of a merry-go-round having a moment of inertia 320 kg m2 and a radius of 4.0 m. The merry-go-round is initially at rest. The boy then starts to walk counter-clockwise around the edge of the merry-go-round at a constant speed of 2.0 ms-1. BPHE-101/PHE-01 3 P.T.O.

4 (i) (ii) In what direction and with what angular speed does the merry-go-round rotate? How much work does the boy do to set himself and the merry-go-round in motion? 4+2=6 2. Attempt.any one part : 1x5=5 (a) (b) A star moves in a circular orbit with a time period of 20 hours about another massive star whose mass is 2.0 x 10 3 kg. Use Kepler's third law to calculate the distance between the two stars. 5 Write down the expression for the centre of mass of an N-particle system. Three particles of equal mass are placed at the vertices of an isosceles right-angled triangle. Determine the centre of mass of the system. 1+4=5 3. (a) A particle A of mass m collides elastically with another particle B of mass 4 m which is initially at rest. After the collision B moves at an angle 0 with the initial direction of motion of A. Determine the direction in which A moves after the collision. If the initial speed of A is pi, determine the speeds of the two particles after the collision. OR BPHE-101/PHE-01 4

5 Two astronauts, each of mass 60 kg, are tied by a light rope and the distance between them is 10 m. They are isolated in space and orbiting their c.m. (centre of mass) at a speed of 6 ms-1. Calculate the angular momentum and kinetic energy of the system. After a while they move closer to each other so that the distance between them is 5.0 m. What is the new angular momentum of the system? What are the new speeds? What is the kinetic energy of the system now? (b) A bird of mass 0.5 kg is flying due north at the latitude 30 N at a speed of 2 ms -1. Determine the Coriolis force acting on it in the Earth's rotating frame. OR A child of mass m stands at rest in a lift moving downward with an acceleration 6 ms-2. Determine the apparent weight of the child. Draw the free body diagram. Take g = 9.8 ms =3 BPHE-101/PHE-01 5 P.T.O.

6 titoch (t.71:11:ft.) tifiv tii-a, 2015 lichvirṟt ITRT: f " : 25 7-)F: FTC-A'1 'clfwcf 511w1 a* 3-6* F1174 f 777 TrdW cwill-et TT H/Aqi T 47(160,?ej g27-77-r / 1. ITRE W7 : 2x6=12 () (i) off HRirtgcl tve 71-1 grid : 44-Zi qr1 -F-kifur- -41-r 7LP:I t, cater 1-ft 7LP4 6) 4 11 I " 341R =2 (ii) 50 kg *: 444-ii.I cilcs) 574i tr-& 4N-r 3* Pis* 41,4 Trra * 01 t, 4F-d7 -r-qrr 3T- T -4rr lt-q4 -WA? -ftkvr atr'u Ift ci-w I 1+1=2 BPHE-101/PHE-01 6

7 (iii) * -TT Tee m t qn. qt 1:1T-2R 3TC*1 t 1:1T-2TT alluff cakul 100 rad s-2 t 2.0 s Arq t1t-9-tt? 2 (i) 41r4 trt ' -ct PR4 ITT ccrui 1.60 ms -2 TIT9T t 3-11T 3.114)1 7.4 x 1022 kg *, c 7{41- -r- ft TEfT 1? (G = 6.67 x Nm2 kg-2) 2 (ii) T-41 (Nreti-m) T T qc-t : F = (- kix - k2x2) 1:111Z d)ai rb eq fit f-a7 I (Tr) chi4-.i»i1 Si tr77 I 010 kg * T6F4 uy4t t I 764 tft Aci4 ' chlkul Tt. a ft 'iii giu feral TrziT 4, J t I 20 m *1 'tqr tft tr-d-r4 tact4cid *I -r--a7 ittq Art4 crokui AfffftxT atit co-i g= 10 ms-2 A1177 I 2+4=6 (V) 20 kg pemh am! cischi, 4.0 m fiwit kg m2 icci arrivf Aft-A-468 * f*-41-1 (5151 t I 31*-T ferihicr-21t I fzi,i ,35 1-*711 Lft qrrn-44 rqii A 2.0 ms-1 3T-4T -ctio * BPHE-101/PHE-01 7 P.T.O.

8 fqrr 3 f r -cim 4 Trig *TaT t? (ii) -it-t68 3 3T:A it ct -k4 * I -dm chl4 cht-ii 45(11? 4+2= )1 7-W ITFT 1x5=5 () T Kim 18TWR 4.1-f 4 t I.31.4.)1 atra--4-r-o. 20 t TO, i i. T (:, x 1030 kg t I *1 R 5rzr)Tr c-a * 41-ct s, ch rid W--4RI *T4 *r ceolch I ki ot alrl 4rq cbuil 1: rq 1:11TQl7 f Atli k(gr Trzrr t TA. fr*-tzi "Wf fwd rr7r I 1+4=5 3. () (7,e m am! lq.> chut A, 4 m clic4 71 W:11. B* 1T *EP chkc-ii t 3T-R-L-R 4 WIT B 4 -Pr-dt I TiErp * B, A 3TECTW ttzt cblut cccr iir choi t I*Fa-4* A lirc1 -Pqrr Aulftd A'rr-A-R leir A atftr 1:41(1 t, t *IF 1-q 311 chuli mnri 1-4tfta Arr--4R 311 MT BPHE-101/PHE-01 8

9 3i-aft4T-en, T4:1 TR:ft t kg 10 mm aidftk-t 4 -ft-4m t att ater4 TṬR-4)-t -tritwqr 6 ms-1 chtfi I wr fir * 3T1T 40\4 *'t 11--AR vs. atr -% A'm AI )( 5.0 intg Aid) I r Tzff wi:rftzt (-idq err'? -ftwrzi t1,31 d)\31 3T4 WdtX14? 5 NO 0.5 kg WI 30 N 3.1.4ft art tut- 4 2 ms-1 qim :41 1. A zutrt =11-4R 3 ater4t m qi II TrT fucre 34-{ cakui 6 ms-2 Tr aim *, rawila-41 4 t 3TrITR41 RR W-AR aft -4.r-4RI g = 9.8 ms-2 #If7R I 2+1=3 BPHE-101/PHE-01 9 P.T.O.