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

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Quantrex Academy · Accepted Answer

Correct answer: D. ((5)/(9))4u

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

{v}_{2} = \dfrac{{u}_{1}\left(1 + e\right){m}_{1}}{( {m}_{1} + {m}_{2} )} + {u}_{2}\dfrac{( {m}_{2} - {m}_{1}e )}{( {m}_{1} + {m}_{2} )}

In present problem

{u}_{2} = 0, {m}_{2} = 2{m}_{1}

and , hence

{v}_{2} = \dfrac{u\left(1 + \dfrac{2}{3}\right){m}_{1}}{( {m}_{1} + 2{m}_{1} )} = \dfrac{5}{9}u

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

{v}_{5} = {\left(\dfrac{5}{9}\right)}^{4}u

The masses of five balls at rest and lying at equal distances in a...

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