A monkey of mass $m=15\text{ kg}$ climbs a rope which can withstand a maximum tension of $T_{\text{max}}=200\text{ N}$. What is the maximum acceleration $a$ with which the monkey can climb up the rope? (Take $g=10{\text{ m/s}}^2$)

Solution

1. Identify the given values: mass $m=15\text{ kg}$, maximum tension $T_{\text{max}}=200\text{ N}$, and acceleration due to gravity $g=10{\text{ m/s}}^2$.
2. Apply Newton's second law for the upward motion: $T_{\text{max}}-mg=ma$.
3. Substitute the known values into the equation: $200-(15\times 10)=15a$.
4. Simplify the equation to solve for $a$: $200 - 150 = 15a$, which gives $50 = 15a$.
5. Calculate the final acceleration: $a=\frac{50}{15}\approx 3.33{\text{ m/s}}^2$.
6. Hence the answer is (C).