Two blocks of mass `m_(1)` and `m_(2)` `(m_(1) lt m_(2))` are connected with an ideal spring on a smooth horizontal surface as shown in figure. At t = 0 `m_(1)` is at rest and `m_(2)` is given a velocity v towards right. At this moment, spring is in its natural length. Then choose the correct alternative :

Options

A. Block of mass `m_(2)` will be finally at rest after some time.
B. Block of mass `m_(2)` will never come to rest.
C. Both the blocks will be finally at rest.
D. None of these

Explanation

If velocity of `m_(2)` is zero then by momentum conservation `m_(1)v'=m_(2)v`
`v'=(m_(2)v)/(m_(1))`
Now, kinetic energy of `m_(1)`
`=1/2 m^(1)v'^(2)=1/2 m_(1)((m_(2))/(m_(1)))^(2)v^(2)=1/2((m_(2))/(m_(1)))m_(2)v^(2)=((m_(2))/(m_(1)))1/2 m_(2)v^(2)=(m_(2))/(m_(1))xx` intial kinetic energy
Kinetic energy of `m_(1) gt` initial mechanical of system Henced proved