Question

A monkey of mass 40 kg climbs on a massless rope which can stand a maximum tension of 500N. 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 $5m{s}^{-2}$
• B. The monkey climbs down with an acceleration of $5m{s}^{-1}$
• C. The monkey climbs up with a uniform speed of $5m{s}^{-1}$
• D. The monkey falls down the rope freely under gravity.

Answer 1

Answer: (A)

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

Here, mass of monkey, m=40 kg
Maximum tension the rope can stand, T=500N
Tension in the rope will be equal to apparent weight of the money (R).
The rope will break when R exceeds T.

(a) When the monkey climbs up with an acceleration a=5$m{s}^{-2}$
$R=m(g+a)=40(10+5)=600N\therefore$ R>T
Hence, the rope will break.

(b) When the monkey climbs down with an acceleration a=5$m{s}^{-2}$
$R=m(g-a)=40(10-5)=200N\therefore$ 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
$\therefore$ R=mg=$40\times 10=400N\therefore$ R<T
Hence, the rope will not break.

(d) When the monkey falls down the rope freely under gravity, a=g $\therefore R=m(g-a)=m(g-g)=zero$

Hence, the rope will not break.