Question

A monkey of mass $40kg$ climbs on a rope. The rope can stand a maximum tension of $600N$. In which of the following cases will the rope break:

• A. climbs up with an acceleration of $6m{s}^{-2}$
• B. climbs down with an acceleration of $4m{s}^{-2}$
• C. climbs up with a uniform speed of $5m{s}^{-1}$
• D. falls down the rope nearly freely under gravity

Answer 1

The correct option is A

climbs up with an acceleration of $6m{s}^{-2}$

Explanation for the correct option:

Step 1: Given data in the question.

In the question, it is given that a monkey of mass $40kg$ climbs on a rope and the rope can stand a maximum tension of $600N$.

Step 2: Concept to be used.

The tension in an inextensible and weightless string can be given by the sum of the weight hanging from it and the force acting on it.

Step 3: Find the maximum acceleration at which the monkey can climb the rope without breaking it.

Assume that it monkey is climbing in the upward direction with the acceleration of $am{s}^{-2}$.

So, the total tension $T$ on the rope is given as:

$T=mg+ma$ where $m$is the mass of the monkey.

Since, the mass of the monkey is $40kg$ and the maximum tension rope can handle is $600N$.

So,

$$\begin{gathered} 600=40\times 10+40a \\ \Rightarrow 600=400+40a \\ \Rightarrow 200=40a \\ \Rightarrow a=5 \end{gathered}$$

Therefore, the maximum acceleration at which the monkey can climb the rope is $5m{s}^{-2}$.

Since, In the option $A$ it is given that the monkey climbs up with an acceleration of $6m{s}^{-2}$ which is greater than the maximum allowed acceleration.

Therefore, the rope will break when the monkey climbs up with an acceleration of $6m{s}^{-2}$ .

Hence, option $A$ is the correct answer.