Question

A block of mass m rests on a rough horizontal surface with a rope tied to it. The co-efficient of friction between the surface and the block is $\mu$. A monkey of the same mass climbs at the free end of the rope. The maximum acceleration with which the monkey can climb without moving the block is

• A. $\frac{\mu g}{\mu sin\theta +cos\theta }-g$
• B. $\frac{\mu g}{\mu sin\theta -cos\theta }+g$
• C. $\frac{\mu g}{tan\theta -\mu cos\theta }+g$
• D. $\frac{\mu g}{tan\theta +\mu sec\theta }-g$

Answer 1

The correct option is A

$\frac{\mu g}{\mu sin\theta +cos\theta }-g$

$T-mg=ma.........\left(1\right)Tcos\theta =\mu (mg-Tsin\theta )T=\frac{\mu mg}{(cos\theta +\mu sin\theta )}NowputtingvalueofTinequation\left(1\right)a=\frac{\mu g}{Nsin\theta +cos\theta }-g$