A light string fixed at one end to a clamp on ground passes over a fixed pulley and hangs at the other side. It makes an angle of $30^{o}$ with the ground. A monkey of mass $5 k g$ climbs up the rope. The clamp can tolerate a vertical force of $40 N$ only. The maximum acceleration in upward direction with which the monkey can climb safely is (Neglect friction and take $g = 10 {m s}^{- 1}$

2 {m s}^{- 2}

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4 {m s}^{- 2}

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6 {m s}^{- 2}

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8 {m s}^{- 2}

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Solution

The correct option is C $6 {m s}^{- 2}$
$\begin{matrix} L e t T b e t h e t e n s i o n o n t h e s t r i n g . N o w, t h e u p w a r d f o r c e e x e r t e d o n t h e c l a m p = T sin 30^{0} = \frac{T}{2} a n d, A c c o r d i n g t o q u e s t i o n . . . . . . . . . . . . . . . \Rightarrow \frac{T}{2} = 40 N \Rightarrow T = 80 N N o w, i f a b e t h e a c c e l e r a t i o n o f t h e m o n k e y i n u p w a r d d i r e c t i o n, t h e n, a = \frac{T - m g}{m} = \frac{80 - (5 \times 10)}{5} = 6 m / s^{2} \end{matrix}$
so that the option is C.

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