Question

A monkey of mass $40\text{kg}$ climbs up a rope of breaking load $600\text{N}$, hanging from a ceiling. If it climbs up the rope with maximum possible acceleration, then the time taken by the monkey to climb up is:
(Length of the rope is $10\text{m}$ and $g=10{\text{m/s}}^2$).

• A. $1\text{s}$
• B. $3\text{s}$
• C. $4\text{s}$
• D. $2\text{s}$

Answer 1

The correct option is D $2\text{s}$

Monkey will climb up with maximum acceleration $\left(a\right)$, when it pulls the rope with maximum force which is equal to breaking strength $600\text{N}$.
$\therefore$ Rope will pull monkey upwards with maximum force of $600\text{N}$.
i.e $T=600\text{N}$
FBD of monkey:


$T-mg=ma$
$\Rightarrow 600-40\times 10=40a$
$\therefore a=\frac{200}{40}=5{\text{m/s}}^2$
Now, applying kinematic equation:
Length of rope $l=10\text{m}$
$10=ut+\frac{1}{2}a{t}^2=0+\frac{1}{2}\times 5\times t^2$
$\Rightarrow 5t^2=20$
$\therefore t=\sqrt{4}=2\text{s}$