Question

A boy wants to climb down a rope. The rope can withstand a maximum tension equal to two-thirds the weight of the boy. If $g$ is the acceleration due to gravity, the minimum acceleration with which the boy should climb down the rope is equal to

• A. $\frac{g}{3}$
• B. $\frac{2g}{3}$
• C. $g$
• D. Zero

Answer 1

The correct option is A

$\frac{g}{3}$

Let a be the minimum acceleration with which the boy must climb down the rope.
From the second law of motion, $mg-T=ma\Rightarrow T=m(g-a)........\left(1\right)$
Now, the maximum allowable tension is $\frac{2mg}{3}$. Substituting in equation (1), we get
$\frac{2}{3}mg=m(g-a)\Rightarrow a=\frac{g}{3}$
Hence, the correct choice is (a).