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Two objects of masses 200 g and 500 g possess velocities 10 i^ m s-1 and 3i^+5j^ m s-1, respectively. The velocity of their centre of mass in m s-1 is,

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Important Questions on Centre of Mass, Momentum and Collisions

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Two bodies of different masses 2 kg and 4 kg are moving with velocities 2 m s-1 and 1 m s-1 towards each other due to mutual gravitational attraction. Then the velocity of the centre of mass is
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Two spheres of masses 2M and M are initially at rest at a distance R apart. Due to mutual force of attraction, they approach each other. When they are at separation R2, the acceleration of the centre of mass of spheres would be 
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Two bodies A and B have masses M and m respectively where M>m and they are at a distance d apart. Equal force is applied to them so that they approach each other. The position where they hit each other is _____.
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Two balls A and B of masses 100 gm and 250 gm respectively are connected by a stretched spring of negligible mass and placed on a smooth table. When the balls are reléased simultaneously the initial acceleration of B is 10 cm sec-2 west ward. What is the magnitude and direction of initial acceleration of the ball A -
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A shell of mass m moving with velocity u suddenly breaks into 2 pieces. The part having mass m4 remains stationary. The velocity of the other part of the shell will be
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A stone is projected with an initial velocity at an angle to the horizontal. A small piece separates from the stone before the stone reaches its maximum height. Then this piece will
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Three particles with masses 10, 20 and 40 gm are moving with velocities 10i^, 10j^ and 10 k^ m sec-1, respectively. If due to some interaction the first particle comes to rest and the velocity of second becomes (3i^+4j^) m s-1 then the velocity of third particle after the interaction is:
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Two particles having mass ratio n:1 n>1 are interconnected by a light inextensible string that passes over a smooth pulley. If the system is released, then the acceleration of the centre of mass of the system is