Question

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

• A. When the monkey climbs with constant speed of $5m{s}^{-1}$
• B. When the monkey climbs with constant acceleration of $2m{s}^{-1}$
• C. When the monkey climbs with constant acceleration of $5m{s}^{-1}$
• D. When the monkey climbs with constant speed of $12m{s}^{-1}$

Answer 1

Answer: (A)

When the monkey climbs with constant speed of $5m{s}^{-1}$

$\begin{array}{c}\text{Monkey is going to apply}\\ \text{an equal and opposite pseudo force}\\ \text{on the rope}\overline{m}\text{downward direction}\\ \begin{array}{c}T⩾m(g+a_p)..........(a_p=a)\\ \Rightarrow T⩾m(g+a)\\ \Rightarrow \frac{T}{m}⩾(g+a)\end{array}\end{array}$

$\Rightarrow 3\cdot 33⩾\text{(Putting in values from question)}$

$\begin{array}{c}\text{Hence acceleration of the monkey must be less than}3.33m/s^2\\ \text{in order to prevent the rope from breaking.}\end{array}$

$\text{Hence Ans is (}A\text{)}$