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 O from the ceiling is y and the distance of point O from each pulley is x and the distance between the two pulleys is l.
`x^(2) = y^(2) + (l^(2))/(4)`
Differentiating the above equation w.r.t to "t"
`2x((dx)/(d t)) = 2y((dy)/(dt)) + (1)/(4) 2l((dl)/(d t))`
But, `u = -(dx)/(dt), v = (dy)/(dt)` and `(dl)/(d t)`
`therefore - x u = y u` and `v = -u(x)/(y) = u sec theta`
`therefore` Velocity of mass `= v = u sec theta` (upwards)