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.

In the arrangement shown in figure the ends of an in extensible string

1.	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.
Answer» Solution :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)