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.

Find velocity of block `A` will be `:`

Options

A. `2.5 hat(i) m//s`
B. `-1.8 hat(i) m//s`
C. `3.6 hat(i) m//s`
D. `-3.4 hat(i) m//s`

Answer

D

Explanation

`(1)/(2)xx2xx5^(@)+(1)/(2)(3)2^(2)=(1)/(2)xx2V_(1)^(2)+(1)/(2)3xxV_(2)^(2) ....(2)`
`2(5)-3(2)=2V_(1)+3V_(2) …(3)`
`V_(1)=-3.4hat(i)`