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Two spheres ‘A’ and ‘B’ of equal mass lie at rest at the opposite ends of a diameter of a smooth horozontal circular groove of radius ‘r’. ‘A’ move and collides with ‘B’ after a time ‘t’. If ‘e’ is the coefficient of restitution, next, collision between the spheres takes place after a time of ______.

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$\frac{2 t}{e}$

$\frac{πt}{e}$

$\frac{2 πt}{e}$

$\frac{t}{e}$

answer is A.

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Detailed Solution

The relative velocities of the bodies determine how long it takes to go a distance.
From the question,

$πr = tu$

By using the equation of e,

$e = \frac{v_{2} - v_{1}}{u} v_{2} - v_{1} = u e t i m e r e q u i r e d = \frac{2 πr}{u e} = \frac{2 t}{e} .$

Hence the correct answer is $\frac{2 t}{e} .$

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