A spring is compressed between two toy carts of mass `m_(1)` and `m_(2)`. When the toy carts are released, the springs exert equal and opposite average forces for the same time on each toy cart. If `v_(1)` and `v_(2)` are the velocities of the toy carts and there is no friction between the toy carts and the ground, then :

Options

A. `v_(1)//v_(2)=m_(1)//m_(2)`
B. `v_(1)//v_(2)-m_(2)//m_(1)`
C. ` v_(1)//v_(2)=-m_(2)//m_(1)`
D. `v_(1)//v_(2)=-m_(1)//m_(2)`

Answer

C

Explanation

Applying law of conservation of momentum
`mv_(1)v_(1)+m_(2)v_(2)=0, (m_(1))/(m_(2))=-(v_(2))/(v_(1)) or (v_(1))/(v_(2))=-(m_(2))/(m_(1))`