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

see full answer

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

$\frac{m g}{4 h} \sqrt{d^{2} + 4 h^{2}}$

hmg

dmg

$\frac{m g}{2 h} \sqrt{h^{2} + d^{2}}$

answer is A.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

From the free body diagram,

$F cosθ + F cosθ - m g = 0$

$2 F cosθ = m g$

So, as the man moves up, $θ$ increases, cos $θ$ decreases.

$∵ cosθ = \frac{h}{\sqrt{{(\frac{d}{2})}^{2} + h^{2}}}$

Now, when the man is at depth h, then the force is

$F = \frac{m g}{2 \cos θ} = \frac{m g \sqrt{h^{2} + \frac{d^{2}}{4}}}{2 h} = \frac{m g}{4 h} \sqrt{d^{2} + 4 h^{2}}$

Watch 3-min video & get full concept clarity