Question

A monkey of mass $40 \,kg$ climbs ona massless rope which can stand a maximum tension of $500 \,N$. In which of the following cases will the rope break?
(Take$\, g=10\,m \,s^{-2}$)

• A. The monkey climbs up with an acceleration of $5\,m$ $s^{-2}$
• B. The monkey climbs down with an acceleration of $5\,m$ $s^{-2}$
• C. The monkey climbs up with a uniform speed of $5\,m$ $s^{-1}$
• D. The monkey falls down the rope freely under gravity

Answer 1

Answer: (A)

Here, mass of monkey, $m = 40\, kg$
Maximum tension the rope can stand, $T = 500 \,N$
Tension in the rope will be equal to apparent weight of the monkey $(R)$.
The rope will break when $R$ exceeds $T$.
(a) When the monkey climbs up with an acceleration $a=5\,m$ $s^{-2}$
$R=m$ $\left(g+a\right)$ $=40\left(10+5\right)$ $=600\, N$ $\therefore $ $R >T$
Hence, the rope will break.
(b) When the monkey climbs down with an acceleration $a=5 \,m$ $s^{-2}$
$R=m$ $\left(g-a\right)$ $=40\left(10-5\right)$ $=200\, N$ $\therefore \quad$ $R \,< \,T$
Hence, the rope will not break.
(c) When the monkey climbs up with a uniform speed $v=5\, m$ $s^{-1}$, its acceleration $a$ = 0
$\therefore \quad$ $R=mg$ $=40\times10$ $=400\, N$ $\therefore \quad$ $R \,< T\, $
Hence, the rope will not break.
(d) When the monkey falls down the rope freely under gravity
$a=g $ $\,$ $\therefore \quad$ $R=m\left(g-a\right)=m\left(g-g\right)$=zero
Hence, the rope will not break.