A block 'A' of mass M moving with speed u collides elastically with block B of mass m which is connected to block C of mass m with a spring. When the compression in spring is maximum, the velocity of block C with respect to block A is (neglect friction) :-

Options

A. zero
B. `M/M + m u`
C. `(m/M+ m)u`
D. `m/Mu`

Answer

`(3)`

Explanation

`v_(2) = ((2m_(1))/(m_(1) + m_(2))u_(1) + ((m_(2) - m_(1))/(m_(1) + m_(2)))u_(2)`
`v_(B) = ((2M)/(M + m))u`
As the compression is maximum, both B and C move with common velocity `(v_(B) = v_(C))`
`therefore ((2M)/(M+ m))u = (m + m)v_(C)`
`v_(C) = ((Mu)/(M + m))`