Question

A man is sitting in a cabin swinging from a frictionless pulley $P$ as shown in figure. The rope attached with cabin passes over the pulley and is by the man. Total mass of the man and the cabin is $95\text{kg}$. The man wants to pull the rope and rise upwards with an acceleration of $1.2{\text{m/s}}^2$. The correct option is : $(g=9.8{\text{m/s}}^2)$

• A. Man should apply a force of $522.5\text{N}$ on the rope
• B. Man should apply a force of $466.5\text{N}$ on the rope
• C. Man should apply a force of $575.5\text{N}$ on the rope
• D. Man should apply a force of $1050\text{N}$ on the rope

Answer 1

The correct option is A Man should apply a force of $522.5\text{N}$ on the rope

Using Newton's second law for system ( man and cabin together)
$2T-Mg=Ma$

$T=\frac{M(g+a)}{2}=522.5\text{N}$