Question

A rope which can withstand a maximum tension of 400 N is hanging from a tree. If a monkey of mass 30 kg climbs up the rope, in which of the following cases will the rope break? Take $g=10m{s}^{-2}$ and neglect the mass of the rope.

• A. The monkey climbs up with a uniform speed of $5m{s}^{-1}$.
• B. The monkey climbs up with a uniform acceleration of $2m{s}^{-2}$.
• C. The monkey climbs up with a uniform acceleration of $5m{s}^{-2}$.
• D. The monkey climbs down with a uniform acceleration of $5m{s}^{-2}$.

Answer 1

The correct option is C

The monkey climbs up with a uniform acceleration of $5m{s}^{-2}$.

Mass of monkey, $m=30kg$
Acceleration due to gravity, $g=10m{s}^{-2}$
If the monkey climbs up the rope with a uniform acceleration a, the tension in the rope is T = m(g + a). If he climbs down with a uniform acceleration a, the tension is T = m(g - a).
In case (a), since the speed is uniform, a = 0. Therefore, $T=mg=30\times 10=300N$
In case (b), the tension is given by $T=m(g+a)=30\times (10+2)=360N$
In case (c), the tension is given by $T=m(g+a)=30\times (10+5)=450N$
In case (d), the tension is given by $T=m(g-a)=30\times (10-5)=150N$
Since the rope can withstand a maximum tension of 400 N, the rope will break only in case (c). Hence, the correct choice is (c).