Question

A monkey is descending from the branch of a tree with constant acceleration. If the breaking strength of branch is $75\%$ of the weight of the monkey, the minimum acceleration with which monkey can slide down without breaking the branch is

• A. $g$
• B. $\frac{3g}{4}$
• C. $\frac{g}{4}$
• D. $\frac{g}{2}$

Answer 1

The correct option is C $\frac{g}{4}$

Let $T$ be the tension in the branch of a tree when monkey is descending with acceleration $a$.
Then using Newtons second law,
$mg-T=ma$;

For minimum acceleration, tension should be maximum.
Given that breaking strength of the string is $T=75\%$ of weight of monkey
$\therefore ma=mg-\left(\frac{75}{100}\right)mg=\left(\frac{1}{4}\right)mg$
$\Rightarrow a=\frac{g}{4}$