a small particle moving with velocity $v$ collides elastically with a spherical body of equal mass m and radius r initially kept.at rest. The small particle collides at height $h < r$ from the center of the spere as shown fig. Find the final velocities of the two particles.

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Solution

$V e l o c i t y o f t h e s m a l l p a r t i c l e a l o n g t a n g e n t i a l d i r e c t i o n r e m a i n s s a m e = v s i n θ = v \frac{h}{r} C o n s e r v i n g l i n e a r m o m e n t u m a l o n g r a d i a l d i r e c t i o n m v c o s θ = m V_{m r} + m V_{M} s i n c e t h e c o l l i s i o n i s e l a s t i c \frac{V_{M} - V_{m r}}{0 - v c o s θ} = - 1 \Rightarrow V_{M} = V_{m r} + v c o s θ \Rightarrow V_{m r} = \frac{(m - m) v c o s θ}{m + m} = 0 V_{M} = v c o s θ = v \sqrt{1 - {(\frac{h}{r})}^{2}} V_{m} = v s i n θ = v \frac{h}{r}$

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a small particle moving with velocity v collides elastically with a spherical body of equal mass m and radius r initially kept.at rest. The small particle collides at height h<r from the center of the spere as shown fig. Find the final velocities of the two particles.

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a small particle moving with velocity $v$ collides elastically with a spherical body of equal mass m and radius r initially kept.at rest. The small particle collides at height $h < r$ from the center of the spere as shown fig. Find the final velocities of the two particles.