Question

A painter of mass m stands on a platform of mass $m$ and pulls himself up by two ropes which hung over pulley as shown. He pulls each rope with force $F$ and moves upward with a uniform acceleration $a$. Find $a,$ neglecting the fact that no one could do this for long time.

• A. $\frac{4F+(2M+m)g}{M+2m}$
• B. $\frac{4F+(M+m)g}{M+2m}$
• C. $\frac{4F-(M+m)g}{M+m}$
• D. $\frac{4F-(M+m)g}{2M+m}$

Answer 1

The correct option is C $\frac{4F-(M+m)g}{M+m}$

$\begin{array}{c}2F+N-mg=ma----\left(1\right)\\ N=ma+Mg-2F\\ and,\\ 2F-Mg-N=ma---\left(2\right)\\ \\ solving\left(1\right)and\left(2\right)\\ 2F-Mg-\left[ma+mg-2F\right]=ma\\ f-\left(M+m\right)g=\left(M+m\right)a\\ a=\frac{4F-\left(M+m\right)g}{M+m}\\ Hence,theoptionCiscorrectanswer.\end{array}$