A ball of mass `m` moving with speed `v_(0)` strikes a block of mass `3 m` kept at rest. The collision is completely inelastic . If `k` is spring constant , the maximum compression of the spring is

Options

A. `sqrt((mv_(0)^(2))/(k))`
B. `sqrt((mv_(0)^(2))/(2k))`
C. `sqrt((mv_(0)^(2))/(3k))`
D. `sqrt((mv_(0)^(2))/(4k))`

Answer

B

Explanation

By the momentum conservation
`mv_(0) = (m + 3m)v rArr v = (v_(0))/(4)`
`(1)/(2) ( m + 3m)v^(2) = (1)/(2) k x_(0)^(2)`
`4m((v_(0))/(4))^(2) = (mv_(0)^(2))/(4) = k x_(0)^(2)`
`x_(0) = sqrt((mv_(0)^(2))/(4 k))`