The masses of five balls at rest and lying at equal distances in a straight line are in geometrical progression with ratio 2 and their coefficients of restitution are each 2 3 . If the first ball be started towards the second with velocity u , then the velocity communicated to 5 th ball is

Question

The masses of five balls at rest and lying at equal distances in a straight line are in geometrical progression with ratio 2 and their coefficients of restitution are each 2 3 . If the first ball be started towards the second with velocity u , then the velocity communicated to 5 th ball is, 5 9 u, 5 9 2 u, 5 9 3 u, 5 9 4 u

MARKS App · Accepted Answer

We know that velocity of 2nd ball after collision is given by v 2 = u 1 1 + e m 1 ( m 1 + m 2 ) + u 2 ( m 2 - m 1 e ) ( m 1 + m 2 ) In present problem u 2 = 0 , m 2 = 2 m 1 and , hence v 2 = u 1 + 2 3 m 1 ( m 1 + 2 m 1 ) = 5 9 u As four exactly similar type of collisions are taking place successively, hence velocity communicated to fifth ball v 5 = 5 9 4 u

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