In the arrangement shown in figure, 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

(a) `2U cos theta` (b) `(U)/(cos theta)` (c) `(2U)/(cos theta)` (d) `U cos theta`

Explanation

Suppose the distance of point Ofrom the ceiling is y and the distance of point Ofrom each pulley is x and the distance between the two pulleys is
`x^(2)=y^(2)+(1^(2))/(4)`

Differentiating the above equation w.rt to
`2x((dx)/(dt))=2y((dy)/(dt))+(1)/(4)2l((dl)/(dt))`
But `u=-(dx)/(dt), v=(dy)/(dt) and u sec theta`
`:. -xu=yv and v=-u(x)/(y)=u sec theta`
`:.` Velocity of mass `=v=u sec theta` (upward)