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Question

# A block of wood of mass M is suspended by means of a thread. A bullet of mass m is fired horizontally into the block with a velocity v. As a result of the impact, the bullet is embedded in the block. The block will rise to vertical height given by

A

12g(mvM+m)2

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B

12g(mvMm)2

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C

12gmv2(M+m)

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D

12gmv2(Mm)

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Solution

## The correct option is A 12g(mvM+m)2 Let V be the velocity of the block with the bullet embedded in it at the time of impact. From the principle of conservation of momentum, we have mv=(M+m)V ⇒V=mv(M+m) .... (i) If the block, with the bullet embedded in it, rises to a vertical height h, then from the principle of conservation of energy, we have 12(M+m)V2=(M+m)gh ⇒V=√2gh Using (i) and (ii), we get √2gh=mv(M+m) ⇒h=12g(mvM+m)2 Hence, the correct choice is (a).

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