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

Let Force exerted by a monkey is equal to T.

the monkey acceleration upward with acceleration ‘a’

the block, acceleration downward with acceleration a1

[latex] \Rightarrow T − mg − ma = 0 [/latex].

[latex] \Rightarrow T = mg + ma[/latex].

[latex] \Rightarrow T = ma_{11} – mg = 0[/latex].

[latex] \Rightarrow T = mg + ma + ma_{1} – mg = 0[/latex].

[latex] \Rightarrow ma = -ma_{1}[/latex].

[latex] \Rightarrow a = a_{1}[/latex].

Acceleration − a downward, i.e. an upward.

Therefore, both the block and the monkey move in the same direction with equal acceleration. If there is no force exerted by the monkey initially, then there will be no motion of monkey of block occurs as they have the same weight. Hence, their separation will not be changed as time passes.

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