In the figure shown, the cart of mass `6m` is initially at rest. A particle of mass in 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.

Options

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

Answer

C

Explanation

When the rod becomes vertical
`mv_(1)=6mv_(2)impliesv_(1)=6v_(2)`
`=1/2 mv_(1)^(2)+1/26m_(2)^(2)=mgl`
Solve i and ii to get
`v_(rel)=v_(1)+v_(2)=sqrt(7/3gl)`