Each of the blocks shown in figure has mass 1 kg. The rear block moves with a speed of 2 m/s towards the front block kept at rest. The spring attached to the front block is light and has a spring constant 50 N/m. find the maximum compression of the spring.

Explanation

Maximum compression will take place when the blocks move with equal velocity. As no net exterN/Al force acts on the system of the two blocks, the totla linear momentum will remain constant. If V is the common speed at maximum compression we hae ,
`(1kg)(2m/s)=(1kg)V+(1kg)V`
or, `V=1m/s`
INitial kinetic energy `=1/2 (kg)(2m/s)^2=2J`
FiN/Al kinetic energy
`=1/2(1kg)(1m/s)^2+1/2(1kg)(1m/s)^2`
`=1j`
`The kinetic energh lost is stored as the elastic energy in spring.
Hence, `1/2(50N/m)x^2=2J-1=1J`
`or x=0.2m`