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Partially Inelastic Collision

A block of ma...

Question

A block of mass m starts from rest and slides down a frictionless semi-circular track from a height h. When it reaches the lowest point of the track, it collides with a stationary piece of putty also having mass m. If the block and the putty stick together and continue to slide, the maximum height that the block-putty system could reach is:

A

h/4

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B

h/2

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C

h

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D

independent of h

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Solution

The correct option is B h/2
$J u s t b e f o r e t h e c o l l i s i o n t h e v e l o c i t y o f t h e b l o c k i s \sqrt{2 g h} C o n s e r v i n g m o m e n t u m, a s f i n a l l y b o t h t h e b l o c k s a r e m o v i n g t o g e t h e r . m \sqrt{2 g h} = 2 m v \Rightarrow v = \frac{\sqrt{2 g h}}{2} m a x h e i g h t r e a c h e d = \frac{v^{2}}{2 g} = \frac{h}{2}$

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