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A bullet of mass a and velocity b is fir...

A bullet of mass a and velocity b is fired into a large block of mass c. The final velocity of the system is

A

`(m+alpha)/M alpha`

B

`M/(M+alpha) alpha`

C

`(m+M)/m alpha`

D

`m/(m+M)alpha`

Text Solution

Verified by Experts

The correct Answer is:
D
Let `v_1` and `v_2` be the velocities of the body before and after the collision and `v_2 = ev_1 =0.6 v_1`.
and `v_1 =sqrt(2gh) = sqrt(2xx9.8 xx 1)=1.4 m//s`
and `v_2 =0.6 xx1.4 =0.84 ` m/s
For the upward motion, `v_2 =u`
and the maximum height `h_1` reached by the body after rebound is given by
`h_1 =(u^(2))/(2g)=(v_(2)^(2))/(2g)`
`=(0.84xx0.84)/(2xx9.8) =(0.6 xx 0.42)/(7)=0.36`m .
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