Two block `A` and `B` each of mass m are connected by a massless spring of natural length `L` and spring constant `k`. The blocks are initially resting on a smooth horizontal floor with the spring at its natural lengths as shown in fig. A third identical block `C`, alos of mass `m`, moving on the floor with a speed `v` along the line joining `A` and `B` and collides elastically with `A`. Then

Options

A. the kinetic energy of the `A-B` system, at maximum compression of the spring, is zero
B. the kinetic energy of the `A-B` system, at maximum compression of the spring is `(mv^(2))/(4)`
C. the maximum compression of the spring is `v sqrt((m)/(k))`
D. the maximum compression of the spring is `v sqrt((m)/(2k))`

Answer

B, D

Explanation

At the time of maximum compression,
`COLM : m u = 2mv ("for" A "&" B) rArr v = u//2`
`COME : (1)/(2)m u^(2) = (1)/(2) 2mv^(2) + (1)/(2) kx^(2) rArr x = v sqrt((m)/(2k))`