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te, , 1, , KK’s TUITION CENTRE, MEDICAL AND ENGINEERING PHYSICS, FORTNIGHTLY TEST — $5, (Motion of systems of particles and ngid body), , Attempt all questions and each question carries 4marks., Each wrong answer carries (-1) mark., EM._: 120, , Time : 40 min, , Point masses m, and m, are placed at the opposite end of rigid rod of length L and negligible mass. The rod is to, be rotating about an axts perpendicular to it. The position of point P on this rod through which the axis should, pass so that the work required to set the rod rotating with angular velocity w, is minimum, is given by (AIPMTRE 2015), , , , , , , , a) X=m,L'm,, , bd) X=mL(m.tms) °, , c) X=mL(m:+m) Ans:[ ] ‘Se, d) XemLim, je lee, , , , A rod PQ of mass m and length L is hinged at end P. The rod is kept horizontal by a massless string tied to point, (Q.as shown in fig, When the string 1s cut, the initial angular acceleration of the rod ts, , , , a) 2g/L, , b) 2g/3L Ans:[ |, , ©) 322L f &, 4d gL <LI, , , , , , , , A circular dise of moment of inertia |, is rotating in a horizontal plane about its symmetry with a constant angular, speed «, Another disc of moment of inertia [, is dropped coaxially onto the rotating disc Initially the 2nd dise, has zero angular speed. Eventually both the discs rotate with a constant angular speed w,. The energy lost by the, initially rotating dise to friction is, 2h?, ) tam!, a, , ») ote, , Litem 2, 9) hay, , 1_Sph_ 2, 4) 2etty, The centre of mass of a system of three particles of masses |g, 2g and 3g is taken as the origin of the co-ordinate, system. The position vector of a fourth particle of mass 4g such that the centre of mass of the four particle system, lie at the point (1.2.3) is at f+ 2) + 3%) where a is constant. The value of @ is, , a) 103, , b) 9/2. Ans:[ |, , ce) V2,, , d) 73, Moment of inertia of a rod of mass m and length / about its one end is L. [f one fourth of its length is cut away, then moment of inertia of the remaining rod about its end will be, , a) <1., 3, b) =I Anss[ |, , , , Ans:[ J, , , , c) =I, dj =I
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W, , 2, , A ball of mass 0.25 kg attached to the end of a string of length 1.96 m is moving in a horizontal circle. The string, will break if the tension ts more than 25 N. The maximum speed with which the ball can move is, , a) lms., , bp 3mis. Anss[ J, , c) 3.92 mis., , d) Smis., , A thin rod of length L and mass M is held vertically with one end on the floor. [f the lower end is fixed then the, velocity of the other end of the rod when it falls freely wall be, , a) Vou., b) 29h Ans'[ |, ©) J3gL, d) 2/g0, , A hole of radius R/2 is cut from a thin circular plate of radius R and mass M. The moment of inertia of the plate, about an axis through the centre of the plate perpendicular to x-y plane (1.¢., about z-axis) 1s, a) SMR’., 2 MR?, b) SMR Ans-[ |, ©) SMR?, dy) Sr?, 24, , What is the moment of inertia of a solid sphere of density p and radius R about its diameter?, 105,44, , a) Tee, , b) ing? Ans:[ ], a) wer?, d) ek, , A pulley fixed to the roof cartes a string with blocks of masses m, = 3m and m; = m attached to its ends, The, masses of the string and pulley are neghible. When the system is released, the acceleration of C.M. will be, , , , a) Zero “ole, b) -24 Ans:[ J c, , c) g2 “ie f, , 4-2 "bal., , , , , , , , Three identical spheres, each of mass M are placed at the corners of right angled triangle with mutually, perpendicular sides equal to 2 metre. Taking their points of intersection as the origin, the position vector of ¢.m., , is, a) 4@-)), >) 20-7 Ans:[ |, o) 20+), , ) 0+), A square plate of side 20cm has uniform thickness and density. A citcular part of diameter 8cm is cut out, symmetrically as shown in figure. The position of c.m. of the remaining portion is, , a) ato,, , b) ato Ans | | ofa, , c) 0.54 cm towards left from o. "RS, , d) 0.86 cm towards lefi from o.
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13., , 14, , 5, , 9, , 3, , A thin wire of length L and uniform linear mass density p is bent into a circular loop with centre at o as shown in, figure. The moment of inertia of the loop about the axis xx! 1s, , a = x, , 2 f, , » 2 amet i} (I, , Sel’, , SV Sat =, , i?, , ®), , ‘The angular velocity of a fly wheel changes with time as @ = a - bt, where a and b are constants. The angle, through which it rotates before coming to rest 1s, , al aja—b), , b) =, c) 2s Ans: | |, d) =, , 2ab, A thin uniform rod of mass m and length 21. is acted upon by a constant torque The angular velocity changes, from 0 to @ int sec. The torque is m=, , a) mie i, , a i:, b), , , , af, , , , , , , , , , , , , , arte, , , , , , , , t, mia, a, 4 =, A solid cylinder of mass M and radius R rolls down an inclined plane of height h without slipping. The speed of, , its centre of mass when it reaches the bottom is, , a) y2gh, , , , ce) Ans:[ J, , » je, ce) sgh Ans:[ |, a) [Sah, , A sphere of mass 10 kg and radius 0.15 m rotates about a tangent. The moment of inertia of the sphere is, , a) Skg-m?, , b) 2.7 kgm? Ans:[ ], , ©) 3.S kgm?, , d) 4.5 kg-m’, ‘The moment of inertia of two equal masses each of mass m at separation 1. connected by a rod of mass M about, an axis passing through centre and perpendicular to the length of the rod 1s, , a) (8+3m)2?, , l, , (M+6m)e2, —_, ue, me’, d) z, ‘Three thin rod each of length Land mass M are placed along x, y and 7 axes such that one end of each rod ts at, , b), , ce Ans:[ J, , , , origin. The moment of inertia of this system about z-axis is ‘ ;, a) 23M?, b) 4/3 ML* :, ce) S3MI2 Ans-[ | © rd, , , , , , , , , , d) ML/3
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+, , 20. The moment of inertia of a thin rectangular plate ABCD of uniform thickness about an axis passing through the, , 21., , 23., , 24., , 25., , centre o and perpendicular to the plane of the plate ts, a) [41, b) LH:, ce) bt Ans:[ |, d) [yh tls, , , , , , , , , , , , , , , , , , , , , , , , , , If 1, is the moment of inertia of a thin rod about an axis perpendicular to its length and passing through its centre, of mass and I; is the moment of mertia of the ring about an axis perpendicular to the plane of mng and passing, through its centre formed by bending the rod, then, f 3, one, ) ps, f bial, ce) Roa Ans:[ ], h_ x, d) 2=5, ABC is a nght angled triangular plate of uniform thickness, The sides AB>BC as in figure 1), 1; and 1; are, moments of inertia about AB, BC and CA respectively. Then, a) Lebel, 4, b) h>h>h 1,, co) h>h>h Ans-| | 4, d) heheh . zo, ‘Three particles each of mass m are situated at the vertices of an equilateral triangle ABC of side / is in figure., The moment of inertia of the system about the line AY perpendicular to AB in the plane ABC will be, a) ¥4mr, b) 2m? Ans:[ J A, ©) 43 mi J\, dy St nf? A—,, Three rings each of mass M and radius R are arranged as shown in figure. Moment of inertia of the system about, the axis XX’ will be :, a) 7/2MR* Ty, b) 3MR° Ans:[ ] AY, ce} W2MR°, d) SMR®, A square is made by joining four rods each of mass M and length L. [ts moment of inertia about an axis PQ in its, plane and passing through one of its corner as shown in figure is, a) 6ML’ a, b) 4/3ML? Ans:[ ] ef, ce) 8/3MI2 >, d) 10/3ML? ’, . The speed of a homogenous solid sphere after rolling down an inclined plane of vertical height h from rest, without sliding 1s, a) gh, b) Jak, ©) JEgk Ans:[ ]
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5, , 27. The ratio of radius of gyration of a circular disc about a tangential axis in the plane of the disc and of a circular, ning of same radius about a tangential axis in the plane of the ring ts, a) 23, b) 2:1 Ans:[ |, ce) VEG, d) bv?, 28. A particle of mass m is rotating in a plane in a circular path of radius r. Its angular momentum is L. The, centripetal force acting on the particle is, , ) —, = Ans:[ ], ®), 29. If the radius of the earth becomes half of its present value (mass remaining the same), the new length of the day, would be, a) 6h, b) 2h Ans:[ ], co) 48h, d) 96h, 30. A gramophone record is known to revolve at the rate of n revolutions per sec. A small object kept on the record, , has a coefficient of fnetion 1 wrt the record, The minimum distance at which the object must be kept so that it, , may revolve with the record is, emt, z, b) = Ans:[ J, ante, =, d) =, ng, , , , e), , teeeeeeeses
