Question

A man of mass $m$ stands on a crate of mass $M$. He pulls on a light rope passing over a smooth light pulley. The other end of the rope is attached to the crate. For the system to be in equilibrium, the force exerted by the man on the rope will be

• A. $(M+m)g$
• B. $\frac{1}{2}(M+m)g$
• C. $Mg$
• D. $mg$

Answer 1

The correct option is B $\frac{1}{2}(M+m)g$

Force exerted by man on rope transfers to it in the form of tension
From the free body diagram of man and crate system:
For vertical equilibrium: $2T=(M+m)g$ or
$\therefore T=\frac{(M+m)}{2}g$