Question

A $50\text{kg}$ person stands on a $25\text{kg}$ platform. He pulls on the rope which is attached to the platform via the frictionless pulleys as shown in the figure. The platform moves upward at a steady rate if the force with which the person pulls the rope is

• A. $500\text{N}$
• B. $250\text{N}$
• C. $25\text{N}$
• D. $50\text{N}$

Answer 1

The correct option is B $250\text{N}$

Taking platform, person and the pulley connected to it in consideration.
Free body diagram of these can be given as

By force balancing
$3T=(M+m)g$
where
$M=\text{mass of the platform}m=\text{mass of the person}T=\text{tension in the string}$
From we get
$T=\frac{(50+25)10}{3}\Rightarrow T=250\text{N}$