Block C of mass M is moving with velocity `V_(0)` and collides elastically with block A of mass M and connected to another block B of mass 2M through a spring of spring constant K. What is K if `X_(0)` is the compression of spring when velocity of A and B is same

Options

A. `(mv_(0)^(2))/x_(0)^(2)`
B. `(mv_(0)^(2))/(2x_(0)^(2))`
C. `(3)/(2)(mv_(0)^(2))/x_(0)^(2)`
D. `2/3(mv_()^(2))/x_(0)^(2)`

Answer

D

Explanation

`mv_(0)=mv+mv`
` v=v_(0)/2`
`k_(1)+v_(1)=k_(f)+v_(f)`
`1/2mv_(0)^(2)+0=1/2mu((v_(0))/2)^(2)xx2+1/2kx_(0)^(2)`