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.

When the blocks are yet to attain their final velocities, in this situation at any instant when block `A` is moving with a velocity `4 hat(i) m//s` , velocity of block `B` will then be `:`

Options

A. `-1.33 hat(i) m//s`
B. `-2.67 hat(i) m//s`
C. `1.67 hat (i) m//s`
D. `3.77hat(i) m//s`

Answer

A

Explanation

`31=(1)/(2)2xx4^(@)+(1)/(2)xx(3)V_(2)^(2)+(1)/(2)kx^(2) ....(4)`
`(2)5-3(2)=4xx2+3V_(2) .....(5)`
`4-8=3V_(2)-(4)/(3)=V_(2), vec(V)_(2)=-1.33hat(i)`
put `V_(2)` in equation `(4)`