A monkey of mass 40 kg climbs on a 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) 

 

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 , $a=5 m s^{-2}$

$$\begin{gathered} R=m(g+a) \\ =40(10+5) \\ =600 N \\ \therefore R>T \end{gathered}$$

Hence the rope will break.

(b) When the monkey climbs down with an acceleration, $a=5 m s^{-2}$

$$\begin{gathered} R=m(g-a) \\ =40(10-5) \\ =200 N \\ \therefore R<T \end{gathered}$$

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

$$\begin{gathered} R=mg \\ =40\times 10 \\ =400 N \\ \therefore R<T \end{gathered}$$

Hence rope will not break.

(d) When the monkey falls down the rope freely under gravity $a=g$

$$\begin{gathered} R=m(g-a) \\ =m(g-g) \\ =0 \end{gathered}$$

Hence rope will not break.