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. `((3MV_(0)^(2))/(2X_(0)^(2)))`
D. `((2MV_(0)^(2))/(3X_(0)^(2)))`

Answer

D

Explanation

`MV_(0)=3MV`
`V=(V_(0))/(3)`
`-(KX_(0)^(2))/(2)=(1)/(2)(3M)((V_(0))/(3))^(2)-(1)/(2)MV_(0)^(2)=(MV_(0)^(2))/(6)-(MV_(0)^(2))/(2)=-(MV_(0)^(2))/(3)`
`K=((2MV_(0)^(2))/(3x_(0)^(2)))`