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.

Velocity of centre of mass of the system of blocks `A` and `B`, before collision is `:`

Options

A. zero
B. `0.6 hat(i) m//s`
C. `+0.8 hat(i) m//s`
D. `1.4 hat (i) m//s`

Answer

C

Explanation

`V_(CM)=(m_(1)vec(V)_(1)+m_(2)vec(V)_(2))/(m_(1)+m_(2)) .....(1)`
`=((2xx5-3xx2))/(3+2)=+(4)/(5)hat(i)=+.8hat(i)`