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

1. g
2. 3g/4
3. g/4
4. g/2

Correct answer: g/4

Solution

The breaking strength of the branch is 75% of the monkey's weight, i.e., 0.75mg. The net force acting on the monkey is the difference between its weight (mg) and the tension in the branch (T). For the branch to not break, T ≤ 0.75mg. Using Newton's second law, mg - T = ma. Substituting T = 0.75mg, we get mg - 0.75mg = ma, which simplifies to 0.25g = a. Thus, the minimum acceleration is g/4.

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