In the figure shown, the cart of mass 6m is initially at rest. A particle of mass m is attached to the end of the light rod which can rotate freely about A. If the rod is released from rest in a horizontal position shown, determine the velocity `v_(rel)` of the particle with respect to the cart when the rod is vertical. (Assume frictionless surface)

Options

A. `sqrt (7/3gl)`
B. `sqrt(7/6gl)`
C. `sqrt(14/3gl)`
D. `sqrt(8/3gl)`

Answer

A

Explanation

`WD=Deltak`
`mgl=1/2(m.6m)/(m+6m) (v_(1)+v_(2))^(2)-0`
`:.v_(1)+v_(2)=sqrt(7/3gl))`