In figure, a block `A` of mass `2kg` is moving to the right with a speed `5m//s` on a horizontal frictionless surface. Another block `B` of mass `3kg` a massless spring of spring constant `222N//m` attached to it, is moving to the left on the same surface and with a speed `2m//s` . Let us take the direction to the right as the positive `X-` direction. At some instant, block `A` collides with the spring attached to block `B`. At some other instant , the spring has maximum compression and then, finally, blocks move with their final velocities. Assuming that `(i)` the spring force is conservative and so there is no conversion of kinetic energy to internal energy and `(ii)`, no sound is made when block `A` hits the spring, answer the following questions.

Maximum compression of the spring in the collision will be nearly

Options

A. `30cm`
B. `53cm`
C. `72 cm`
D. `36 cm`

Answer

B

Explanation

for Max compression
`(1)/(2)(2)(5)^(2)+(1)/(2)3(2)^(2)=(1)/(2)(2+3)(.8)^(2)+(1)/(2)Kx^(2)`
`x=50cm`