question_answer

A monkey of mass 20 kg is holding a vertical rope. The rope will not break when a mass of 25 kg is suspended from it but will break if the mass exceeds 25 kg. What is the maximum acceleration with which the monkey can climb up along the rope? \[(g=10\text{ }m/{{s}^{2}})\]              [AIPMT 2003]

A) \[25\text{ }m/{{s}^{2}}\]

B) \[2.5\text{ }m/{{s}^{2}}\]

C) \[5\text{ }m/{{s}^{2}}\]

D) \[10\text{ }m/{{s}^{2}}\]

Correct Answer: B

Solution :

Maximum bearable tension in the rope

\[T=25\times 10=250\text{ }N\]

From the figure,

\[T-mg=ma\]

or         \[a=\frac{T-mg}{m}\]

Given,

\[m=20\text{ }kg,\]

\[g=10\text{ }m/{{s}^{2}},\]

\[T=250\text{ }N\]

Hence,

\[a=\frac{250-20\times 10}{20}\]

\[=\frac{50}{20}=2.5\,m/{{s}^{2}}\]