A solid spherical ball rolling without slipping collides elastically with an identical ball at rest, as shown in the figure. Assuming that the frictional forces are small enough to have negligible effect during the instant of collision, calculate, the velocity of each ball along enough time after the collision when each ball is again rolling without slipping.

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Solution

Since the collision is head on elastic between two identical bodies, so the speeds of the two bodies are interchanged. Thus, the second body will start moving with velocity $V_{1}$ after the collision.
$A p p l y i n g c o n s e r v a t i o n o f a n g u l a r m o m e n t u m : m V_{1} R = m V R + I ω = m V R + \frac{2}{5} m R^{2} ω a n d s i n c e t h e b a l l i s r o l l i n g a f t e r l o n g t i m e ω = \frac{V}{R} \Rightarrow m V_{1} R = m V R + \frac{2}{5} m V R \Rightarrow V = \frac{5}{7} V_{1}$

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