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In the arrangement shown in the Fig, the...

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

Text Solution

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As `P` and `Q` move down, the lebgth `1` decreases at the rate of `Um//s`.
From figure, `1^(2) = b^(2) +y^(2)`
Differentiating with respect to time

`21(dl)/(dt) = 2y (dl)/(dt)` (`:' b` is constant)
`:. = (dy)/(dt) = (l)/(y).(dl)/(dt) = (1)/(cos theta).(dl)/(dt) = (U)/(cos theta)`
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