06%20%20-%20%20Dynamics%20%20of%20%20a%20%20System%20%20of%20%20Particles

06%20%20-%20%20Dynamics%20%20of%20%20a%20%20System%20%20of%20%20Particles

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6 DYNAMICS OF A SYSTEM OF PARTICLES Page 1 1 ) The velocity vectors of three particles of masses 5 kg, 10 kg and 15 kg are respectively ( 5, 3, 0 ), ( 1, 1, 2 ) and ( 1, 2, 4 ). Find the velocity of the centre of mass. The velocity- vector components are in m / s. [ March, 1999, March, 1998 ] [ Ans: ( 5 / 3, 11 / 6, 8 / 3 ) ] 2 ) A system is made up of three particles. The respective linear momenta of particles are ^ ^ ^ k 10 j 20 ; i 10 + and ^ k 10 . If the centre of mass of the system is moving with velocity k 90 j 60 i 30 ^ ^ ^ + + , calculate the total mass of the system. [ Oct., 1997, similar in Oct., 1989 ] ( Ans: There is a printing error in the problem. The linear momentum of the third particle should be corrected as 20 ^ k . Then the answer will be mass = 1 / 3 unit. ) 3 ) Find out the centre of mass of a system of two bodies 20 cm apart. The masses of the bodies are 2 kg and 8 kg. [ October, 1996 ] ( Ans: At 4 cm from the 8 kg mass on a line joining the masses. ) 4 ) The forces of 1 N, 2 N, 3 N and 4 N are acting on the
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06%20%20-%20%20Dynamics%20%20of%20%20a%20%20System%20%20of%20%20Particles

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