Question

A man of mass M is standing on a plank kept in a box. The plank and box as a whole has mass m. A light string passing over a fixed smooth pulley connects the man and box. If the box remains stationary, find the tension in the string and the force exerted by the man on the plank.

• A. $\frac{(m+M)g}{2},\frac{(M-m)g}{2}$
• B. $(m+M)g,\frac{(M-m)g}{2}$
• C. $\frac{(m+M)g}{2},(M-m)g$
• D. $(m+M)g,(M-m)g$

Answer 1

The correct option is A

$\frac{(m+M)g}{2},\frac{(M-m)g}{2}$

Let the tension in the string be T and force exerted by the man on plank be N.
For the (m+M) system, net external force is $2T-(m+M)g$.
For equilibrium, $2T-(m+M)g=0\Rightarrow T=\frac{(m+M)g}{2}$
Now, for the man, $Mg=T+N$
Solving we get, $N=\frac{(M-m)g}{2}$