Two identical spheres A and B lie on a smooth horizontal circular groove at opposite ends of a diameter. A is projected along the groove and at the end of time $t$ , strikes on B. If $e$ is the coefficient of restitution, the second impact will occur after a time:

$\frac{2 π t}{e}$

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$\frac{π t}{e}$

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$\frac{t}{e}$

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$\frac{2 t}{e}$

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Solution

The correct option is D
$\frac{2 t}{e}$

First collision occurs at $t = \frac{π R}{u}$

After collision their relative velocity $= e u$

So second collision will occur after $= \frac{2 π R}{e u} = \frac{2 t}{e}$

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Two identical spheres A and B lie on a smooth horizontal circular groove at opposite ends of a diameter. A is projected along the groove and at the end of time t, strikes on B. If e is the coefficient of restitution, the second impact will occur after a time:

The correct option is D 2te First collision occurs at t=πRu After collision their relative velocity =eu So second collision will occur after =2πReu=2te

Two identical spheres A and B lie on a smooth horizontal circular groove at opposite ends of a diameter. A is projected along the groove and at the end of time $t$ , strikes on B. If $e$ is the coefficient of restitution, the second impact will occur after a time:

The correct option is D
$\frac{2 t}{e}$

First collision occurs at $t = \frac{π R}{u}$

After collision their relative velocity $= e u$

So second collision will occur after $= \frac{2 π R}{e u} = \frac{2 t}{e}$