In the arrangement shown in figure the ends of an in extensible move downwards with uniform speed u. pulleys A and B are fixed. Find the speed with the mass M moves upwards.

In the arrangement shown in figure the ends of an in extensible move d

1.	In the arrangement shown in figure the ends of an in extensible move downwards with uniform speed u. pulleys A and B are fixed. Find the speed with the mass M moves 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 beween the two pulleys is `l`. `x^(2)=y^(2)+(1^(2))/(4)""(##AKS_DOC_OBJ_PHY_XI_V01_A_C04_SLV_026_S01.png" width="80%"> Diiferentiating the above EQUATION w.r.t. to "t" `2X((dx)/(dt))=2y((dy)/(dt))+(1)/(4)2l((dl)/(dt))` But, `u=-(dx)/(dt), v+(dy)/(dt) and (dl)/(dt)` `:. -xu = yu and v=-u(x)/(y) = usectheta` `:. VELOCITY of mass = v = usectheta (upwards)