question_answer

A man of mass m is standing on a structure made up of pulley, strings and platform as shown in figure. Find the force exerted by the person on the rope, so that the system \[\left( person + structure \right)\] remains in equilibrium.

A)  \[\left( M' +M+m \right)g\]         

B)  \[\frac{\left( M' +M+m \right)g}{g}\]

C)  \[\frac{\left( M' +M+m \right)g}{2}\]      

D)  None of these

Correct Answer: C

Solution :

The free body diagram of the system is shown below By force balance \[T+\frac{T}{2}+\frac{T}{2}=(M'+M+m)g\] \[T=\frac{(M'+M+m)g}{2}\]