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In the arrangement shown in figure the e...

In the arrangement shown in figure the ends P and Q of an inextensible string move downwards with uniform speed u. Pulleys A and B are fixed. The mass M moves upwards with a speed

A

`2Ucostheta`

B

`Ucostheta`

C

`(2U)/(costheta)`

D

`(U)/(costheta)`

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` .
From the figure, `l^(2)=b^(2)+v^(2)`
Differentiating with respect to time
`2lxx(dl)/(dt)=2bxx(db)/(dt)+2yxx(dy)/(dt)((As(db)/(dt)=0,(dl)/(dt)=u))`
implies `(dy)/(dt)=((l)/(Y))xx(dl)/(dt)` implies `(dy)/(dt)=((1)/(costheta))xxU=(U)/(costheta)` .
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Knowledge Check

  • 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

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