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q2 r'ACE MEDICAL I MHT-CET Only one option is correct. CENTRE OF MASS & COLLISION EXERCISE - 1 A uniform sphere is placed on a smooth horizontal surface and a horizontal force F is applied on it at a distance h above the surface. The acceleration of the centre IS : (a) maximum when (c) maximum when h=2R (b) maximum when IFR (d) is independent of h A ball kept in a closed box moves in the box making collisions with the walls. The box is kept on a smooth surface. The velocity of the centre of mass : (a) of the box remains constant. (c) of the ball remains constant. (b) of the box-ball system remains constant. (d) of the ball relative to the box remains constant. 3. 4. S. 6. A heavy ring of mass m is fitted onto the periphery ofa light circular disc. A small particle of equal mass is clamped at the centre of the disc. The system is rotated in such a way that center of mass moves in a circle of radius r with a uniiOrm speed v. We conclude that an external larce : (a)mv2 'r must be acting on the central particle (b) 2mv2 /r must be acting on the central particle (d) (2mv2 /r) must be acting on the ring (c) ( 2me 'r) must be acting on the system The centre of mass ofa system of particles is at the origin. It follows that : (a) the number of particles to the right ofthe origin is equal to the lefi of origin. (b) the total mass of the particles to the right of the origin is same as total mass to the left of the origin. (c) the number of particles on the X-axis should be equal to the number of particles on the Y- axts {d) if there is a panicle on the +ve X-axis. there should be atleast one particle on the -ve X axis, None of these. A bead can slide on a smooth straight wire and a particle of mass m is attached to the bead by light string of length L. The particle is held in contact with the wire with the string taut and is then let to fall II' the trad has mass 2m , then when the string makes an angle O with the wire the bead will have slipped a distance. (a) —cosØ) (b) 41 —cosO) —cosO) Two blocks of mass 3 kg and 6 kg respectively are placed on a smooth horizontal surface. They are connected by a light spring of force constant' — 200 N/M. Initially the spring is unstretched, The indicated velocities are imparted to the blocks. The speed of 6 kg block when extension of the spring is maximum will be 2m 6 1.0m 's 2 "g A dog weighting 5 kg is standing on a nat boat so that it is 10 m from the shore. dog walks 4 on the boat towards the shore and then halts. The boat weighs 20 kg and one can assume that 'here is no friction between it and the water. How far is the dog from the shore at the end of this time ? (b) 0.8m (c) 10m CENITRS : MUMBAI /DELHJ 'AKOLA 'LUCKNOW 'NASHIK /PUNE 'NAGPUR # 60