Question

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.

• A. $\sqrt{\frac{14}{3}gl}$
• B. $\sqrt{\frac{7}{6}gl}$
• C. $\sqrt{\frac{7}{3}gl}$
• D. $\sqrt{\frac{8}{3}gl}$

Answer 1

The correct option is C

$\sqrt{\frac{7}{3}gl}$

When the rod becomes vertical

$m{v}_1=6m{v}_2\Rightarrow v_1=6v_2$ .........(i)

$\frac{1}{2}m{v}_1^2+\frac{1}{2}6m{v}_2^2=mgl$ .........(ii)

Solve (i) and (ii) to get $V_{rel}=v_1+v_2=\sqrt{\frac{7}{3}gl}$