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 v cos theta `
B. `v cos theta `
C. `(2v )/( cos theta )`
D. ` ( v )/( cos theta)`

Answer

D

Explanation

Let ` AC = l, AO =a and OC =y`
From the figure
` l^2 =a^2 +y^2 `
Differentating it with respect to time we have
` 2l (dl )/( dt) = 2y ( dy)/(dt) = (1)/( cos theta ) (dl )/( dt) = (v )/( cos theta) " " ( :. (dl)/(dt) =v)`