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Three identical blocks lie at rest along a line on a smooth horizontal surface. The separation between any two adjacent blocks is $L$ . The first block is moved with a velocity $υ$ towards the second block at time $t = 0$ . The coefficient of restitution for collision between any two blocks is 1/3. Then the third block will start moving at time $t = N \frac{L}{u}$ . Find the value of $N$ .

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Detailed Solution

First sphere will take a time $t_{1}$ to start motion in second sphere on colliding with it, where $t_{1} = \frac{L}{u} .$

Now speed of second sphere will be $υ_{2} = \frac{u}{2} (1 + e) = \frac{2}{3} u$

Hence, time taken by second sphere to start motion in third sphere $t_{2} = \frac{L}{2 / 3 u} = \frac{3 L}{2 u} .$

$∴ Totalotimet = t_{1} + t_{2} = \frac{L}{u} + \frac{3 L}{2 u} = \frac{5 L}{2 u}$

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