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In the arrangement shown in Fig. 15.3.15...

In the arrangement shown in Fig. 15.3.15 the ends P and Q of an unstretchable string move downwards with uniform speed U. Pulleys A nd B are fixed. Mass M moves upwards with a speed.

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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)
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