Consider the situation as shown in the diagram. The bullet penetrates the block and emerges with speed `v_(0)//3`. If after collision , the string becomes horizontal , `v_(0)` will be

Options

A. `(m)/(M) sqrt(2 gL)`
B. `(2)/(3) (m)/(M) sqrt( 2gL)`
C. `(3)/(2) (M)/(m) sqrt(2 gL)`
D. `(M)/(m) sqrt(2 gL)`

Answer

C

Explanation

`mv_(0) = Mv_(1) + m(v_(0))/(3) rArr v_(1) = ( 2 mv_(0))/(3 M)`
`0 = v_(1)^(2) - 2 gL`
`((2mv_(0))/(3 M))^(2) = 2gL`
`v_(0) = (3M)/(2m) sqrt( 2gL)`