Two block A and B of masses m and `2m` respectively are connected by a spring of spring cosntant k. The masses are moving to the right with a uniform velocity `v_(0)` each, the heavier mass leading the lighter one. The spring is of natural length during this motion. Block B collides head on with a thrid block C of mass `2m`. at rest, the collision being completely inelastic.

The maximum compression of the spring after collision is -

Options

A. `sqrt((mv_(0)^(2))/(12k))`
B. `sqrt((mv_(0)^(2))/(5k))`
C. `sqrt((mv_(0)^(2))/(10k))`
D. None of these

Answer

(B)

Explanation

At maximum compression, velocity of all block are same & equal to velocity of centre of mass.
`(1)/(2)kx_(m)^(2) = [(1)/(2)mv_(0)^(2) + (1)/(2)(4m) ((v_(0))/(2))^(2)] - (1)/(2)(5m)((3v_(0))/(5))^(2) rArr (1)/(2)kx_(m)^(2) = (1)/(10)mv_(0)^(2) rArr x_(m) = sqrt((mv_(0)^(2))/(5k))`