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

Aicharya · Accepted Answer

We know that velocity of 2nd ball after collision is given by

v_{2} = \frac{u_{1} (1 + e) m_{1}}{(m_{1} + m_{2})} + u_{2} \frac{(m_{2} - m_{1} e)}{(m_{1} + m_{2})}

In present problem

u_{2} = 0, m_{2} = 2 m_{1}

and , hence

v_{2} = \frac{u (1 + \frac{2}{3}) m_{1}}{(m_{1} + 2 m_{1})} = \frac{5}{9} u

As four exactly similar type of collisions are taking place successively, hence velocity communicated to fifth ball

v_{5} = {(\frac{5}{9})}^{4} u

The masses of five balls at rest and lying at equal distances in a straight line are in geometrical…

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