  Question

A monkey is climbing on a rope that goes over a smooth light pulley and supports a block of equal mass at the other end. Show that whatever force the monkey exerts on the rope,the monkey and the block Solution

Suppose the monkey acceleration upward with acceleration '$$a$$' & the block, acceleration downward with acceleration $$a_{1}$$. Let Force exerted by monkey is equal to $$T$$From the free body diagram of monkey$$\therefore T-mg-ma=0$$$$\Rightarrow T=mg+ma$$.Again from the FBD of the block$$T=ma_{11}-mg=0$$$$\Rightarrow T=mg+ma+ma_{1}-mg=0$$ [From (I)] $$\Rightarrow ma=-ma_{1}\Rightarrow a=a_{1}$$Acceleration $$-a$$ downward i.e. $$a$$ upward.$$\therefore$$ The block & the monkey move in the same direction with equal acceleratio.If initially they are rest (no force is exertied by monkey) no motion of monkey of block occurs as they have same weight (same mass). Their separation will not changed as time passes. Physics

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