A man has fallen into a ditch of width d and two of his friends are slowly pulling him out using a light rope and two fixed pulleys as shown in figure. Indicate the correct statements : (assume both the friends apply equal forces of equal magnitude)

Options

A. `(mg)/(4h)sqrt(d^(2)+4h^(2))`
B. hmg
C. dmg
D. `(mg)/(2h)sqrt(h^(2)+d^(2))`

Answer

A

Explanation

(a) `2F cos theta=mg`

`therefore F=(mg)/(2 cos theta)=(mgsqrt(h^(2)+(d^(2))/(4)))/(2h)=(mg)/(4h)sqrt(d^(2)+4h^(2))`