Question

A monkey of mass $20\, kg$ is holding a vertical rope. The rope will not break when a mass of $25\, kg$ is suspended from it but will break if the mass exceeds $25\, kg.$ What is the maximum acceleration with which the monkey can climb up along the rope ? $(g = 10\, m/s^2)$

• A. $5\, m/s^2$
• B. $10\, m/s^2$
• C. $25\, m/s^2$
• D. $2.5 \,m/s^2$

Answer 1

The Correct Option is D

To solve this problem, we need to determine the maximum acceleration with which the monkey can climb the rope without breaking it. Here's how we can approach the solution:

1. The rope can sustain a maximum mass of 25 \, kg, which means the maximum tension the rope can withstand is due to the weight of a 25 \, kg mass. This maximum tension, T, is given by:
   T = 25 \, kg \times g = 25 \times 10 = 250 \, N
2. When the monkey of mass m = 20 \, kg climbs up with an acceleration a, the forces acting on it are the tension in the rope and its weight. The net force acting on the monkey while climbing is the difference between the tension and the weight of the monkey:
   F_{net} = T - m \cdot g
3. According to Newton's second law, this net force is also equal to the mass of the monkey times its acceleration:
   m \cdot a = T - m \cdot g
4. Substitute the known values into this equation:
   20 \cdot a = 250 - 20 \cdot 10
   Simplify the expression:
   20 \cdot a = 250 - 200 = 50
   Thus, solving for a gives:
   a = \frac{50}{20} = 2.5 \, m/s^2
5. Therefore, the maximum acceleration with which the monkey can climb up the rope without breaking it is 2.5 \, m/s^2.

The correct answer is: 2.5 \, m/s^2.