Question

At what minimum acceleration should a monkey slide a rope whose strength is2/3rd at weight​

Answer 1

$\Large\boxed{\sf{3)\quad\!\!\dfrac{g}{3}\ m\ s^{-2}}}$

Solution

Let the mass of the monkey be m so that its weight is W = mg.

For minimum acceleration the tension in the branch should reach its breaking strength, i.e.,

$\longrightarrow\sf{T=\dfrac{2}{3}W}}$

$\longrightarrow\sf{T=\dfrac{2}{3}mg}$

The weight 'mg' is acting downwards, the tension 'T' is acting upwards, and the net force 'ma' is acting downwards as the monkey is descending down. So,

$\longrightarrow\sf{ma=mg-\dfrac{2}{3}\ mg}$

$\longrightarrow\sf{ma=\dfrac{1}{3}\ mg}$

$\longrightarrow\sf{\underline{\underline{a=\dfrac{g}{3}\ m\ s^{-2}}}}$

Answer 2

Let a be the acceleration of monkey.

The apparent weight =mg−ma=2mg/3

or ma=mg(1−2/3)=mg/3⇒a=g/3