Initially spring is in its natural length . The block of mass `3 kg` in contact with rigid wall . The block of mass `1 kg` is pushed through a distance `4 cm` towards the wall and then released. The velocity of the center of mass when the block of mass `3 kg` breaks off the wall is `(k = 100 N//m)`

Options

A. `0.1 m//s`
B. `0.2 m//s`
C. `0.3 m//s`
D. `0.4 m//s`

Answer

A

Explanation

When block `A` is released , spring regains its natural length , speed of `A` is `v_(0) , l` is the natural length of the spring.
By the energy conservation
`(1)/(2) k((4)/(100))^(2) = (1)/(2) xx 1 xx v_(0)^(2)`
`rArr 100((4)/(100))^(2) = v_(0)^(2) rArr v_(0) = 0.4 m//s`
`v_(c.m.) = (1 xx v_(0) + 3 xx 0)/(1 + 3) = (0.4)/(4) = 0.1 m//s`