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A bullet of mass 0.01 kg travelling at a...

A bullet of mass 0.01 kg travelling at a speed of 500 m/s strikes a block of mass 2 kg, which is suspended by a string of length 5 m. The centre of gravity of the block is found to rise a vertical distance of 0.1 m. The speed of the bullet after it emerges from the block will be -

A

`200 m//s`

B

`217 m//s`

C

`204 m//s`

D

`284 m//s`

Text Solution

Verified by Experts

The correct Answer is:
B
Let u and v be velocities of the bullet with which it enters and leaves the block and V is the velocity acquired by the block. Let m and M are masses of the bullet and the block and h is height raised by the block.
`implies mu = mv + mv and 1/2 MV^2 = Mgh implies V = sqrt(2gh) m//s`
`implies v = (mu - MV)/(m) = 500 - (2 sqrt2)/(0.01) = 217 m//s` .
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