Question

A light string fixed at one end to a clamp on the ground passes over a fixed pulley and hangs at the other side. It makes an angle of ${30}^{\circ }$ with the ground. A monkey of mass $5\text{kg}$ climbs up the rope. The clamp can tolerate a vertical force of $40\text{N}$ only. The maximum acceleration in upward direction with which the monkey can climb safely is (neglect friction and take $g=10{\text{m/s}}^2$)

• A. $2{\text{m/s}}^2$
• B. $4{\text{m/s}}^2$
• C. $6{\text{m/s}}^2$
• D. $8{\text{m/s}}^2$

Answer 1

The correct option is C $6{\text{m/s}}^2$

The FBDs of the monkey and clamp are as shown


Let $T$ be the tension in the string.
The upward force exerted on the clamp $=T\sin {30}^{\circ }=\frac{T}{2}$
For $\frac{T}{2}=40\text{N},T=80\text{N}$
If $a$ is the acceleration of monkey in upward direction,
$a=\frac{T-mg}{m}=\frac{80-5\times 10}{5}=6{\text{m/s}}^2$