A monkey is descending from the branch of a tree with constant acceleration. If the breaking strengt

Question

A monkey is descending from the branch of a tree with constant acceleration. If the breaking strength of the branch is $60\%$ of the weight of the monkey,  the minimum acceleration with which the monkey can slide down without breaking the branch is

Professor PC Thomas Classes · Answer

Let $T$ be the tension. Equation of motion for monkey descending: $mg - T = ma$. To not break the branch, max tension $T_{max} = 0.6 mg$. Minimum acceleration required is when $T = T_{max}$. So $mg - 0.6mg = ma_{min} \implies 0.4mg = ma_{min} \implies a_{min} = 0.4g$.