Question

A monkey is decending 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 branch is

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

Answer 1

The Correct Option is C

To solve this problem, we need to determine the minimum acceleration with which the monkey can slide down without the branch breaking. The key details provided are:

• The breaking strength of the branch is 75% of the weight of the monkey.
• The monkey is descending with constant acceleration.

Let's denote:

• \( W \) as the weight of the monkey, which equals \( mg \), where \( m \) is the mass of the monkey and \( g \) is the acceleration due to gravity.
• \( T \) as the tension in the branch when the monkey is descending.

According to the problem, the maximum tension (breaking strength) the branch can handle is:

\( T_{\text{max}} = 0.75 \times W = 0.75 \times mg \)

When the monkey descends with acceleration \( a \), the effective weight (or force exerted) is reduced due to the acceleration. The tension in the branch is given by:

\( T = m(g - a) \)

For the branch not to break, the tension must be equal to or less than the maximum tension:

\( m(g - a) \leq 0.75 \times mg \)

Dividing through by \( m \):

\( g - a \leq 0.75g \)

Rearranging this inequality to solve for \( a \):

\( a \geq g - 0.75g \)

\( a \geq 0.25g \)

Hence, the minimum acceleration with which the monkey can slide down without breaking the branch is:

The correct answer is: \( \frac{g}{4} \) as this is equivalent to \( 0.25g \).