Question

If the breaking strength of a rope is $\frac{4}{3}$ times the weight of a person, then the maximum acceleration with which the person can safely climb up the rope is (g - acceleration due to gravity)

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

Hint:

Breaking strength limits the maximum tension force, which determines max acceleration climbing the rope.

Answer 1

The Correct Option is C

Let the weight of the person be $W = mg$. The breaking strength $T = \frac{4}{3} mg$. The maximum acceleration $a$ is found using: \[ T = m(g + a) \implies \frac{4}{3} mg = m(g + a) \implies g + a = \frac{4}{3} g \implies a = \frac{4}{3} g - g = \frac{g}{3} \]