A man of mass m has fallen into a ditch of width d. Two of his friends are slowly pulling him out using a light rope and two fixed pulleys as shown in figure. Both the friends exert force of equal magnitudes F. When the man is at a depth h, the value of F is

Question

Infinity Learn · Accepted Answer

From the free body diagram,      F $$cos$$θ $$+$$ F $$cos$$θ $$-$$ mg $$=$$ $$0$$                      $$2F$$ $$cos$$θ $$=$$ mgSo, as the man moves up, θ increases, $$cos$$ θ decreases.∵  $$cos$$θ $$=$$ $$hd22$$ $$+$$ $$h2Now$$, when the man is at depth h, then the force $$isF=mg2cos$$θ$$=mgh2+d242h=mg4hd2+4h2$$

A man of mass m has fallen into a ditch of width d. Two of his friends are slowly pulling him out using a light rope and two fixed pulleys as shown in figure. Both the friends exert force of equal magnitudes F. When the man is at a depth h, the value of F is

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