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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

A

`2U cos theta`

B

`U cos theta`

C

`(2U)/(cos theta)`

D

`U/(cos theta)`

Text Solution

Verified by Experts

The correct Answer is:
D
As P and Q fall down, the length l decreases at the rate of Um/s

`l^(2) = b^(2) + y^(2)`
`rArr 2l(dl)/(dt) = 2b(db)/(dt) + 2y(dy)/(dt) [as (db)/(dt) = 0, (dl)/(dt) = U]`
`rArr (dy)/(dt) = l/y xx (dl)/(dt) rArr (dy)/(dt) = U/(cos theta) [as cos theta = y/l]`
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