Q.

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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a

mg4hd2 + 4h2

b

hmg

c

dmg

d

mg2hh2 + d2

answer is A.

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Detailed Solution

From the free body diagram,      F cosθ + F cosθ - mg = 0                      2F cosθ = mgSo, as the man moves up, θ increases, cos θ decreases.∵  cosθ = hd22 + h2Now, when the man is at depth h, then the force isF=mg2cosθ=mgh2+d242h=mg4hd2+4h2
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