In the arrangement shown in the Fig, the ends P and Q of an unstretchable string move downwards with uniform speed U. Pulleys A and B are fixed.
Mass M moves upwards with a speed

Options

A. ` 2 u cos theta`
B. ` u // cos theta`
C. ` 2 u // cos htea `
D. ` u cos theta`.

Answer

B

Explanation

Let ` AB = r, OB = x ` and ` AO = y`.
In ` Delta ABO , r^2 = x^2 + y^2` ltBrgt Differentiating it w.r.t. tiem we get ,`
` ` 2 r (dr)/(dt) =0 + 2 y (dy)/(dt)`
or ` (dy)/(dt) = r/y (dr)/(dt) = (dr)//dt)/(y//r) = u /( cos theta)`.