The ball strikes the block and sticks to it. Find the maximum compression of spring. (`L`: natural length of spring)

Explanation

`x` : maximum compression of spring
By the momentum conservation between `(A)` and `(B)`
`mv_(0) + 2m xx 0 = (m + 2m)v`
`rArr v = (v_(0))/(3)`
By the energy conservation between `(B)` and `(C )`
`(1)/(2) (m + 2m)v^(2) = (1)/(2) kx^(2)`
`x = sqrt((mv_(0)^(2))/(3k)) = v_(0) sqrt((m)/(3k))`