Three identical balls ball I, ball II and ball III are placed on a smooth floor on a straight line at the separation of 10m between balls as shown in figure. Initially balls are stationary. Ball I is given velocity of $10 m/s$ towards ball II. Collision between ball I and II. is inelastic with coefficient of restitution 0.5 but collision between ball III and II is perfectly elastic. The time interval between two consecutive collisions between ball I and II is________ sec.

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Detailed Solution

$e = 0.5, u_{1} = 10 {m/s,u}_{2} = 0 m/s$

$I^{st} case : -$

$v_{1} = (\frac{1 - e}{2}) u$

$= (\frac{1 - 0.5}{2}) 10 = 2.5 m/s$

$v_{2} = (\frac{1 + e}{2}) u = (\frac{1 + 0.5}{2}) 10$

$= 7.5 m/s$

Question Image

Equal masses velocities will interchange

$t = \frac{s}{v} = \frac{100}{75} = \frac{4}{3}$

$v_{3} = 0$

$v_{4} = 7.5 m/s$

Distance between to get 1^st ball with 2^nd

For 2^nd collision $t = \frac{s}{v} = \frac{20}{3 \times 2.5} = \frac{8}{3}$

Remaining distance $= \frac{20}{3}$

Total time $= \frac{8}{3} + \frac{4}{3}$ $= 4 \sec s$

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