In the arrangement shown in figure the ends of an in extensible string move downwards with uniform speed u. Pulleys A and B are fixed. Find the speed with which the mass Mmoves upwards.

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)