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In the figure shown, the lower pulley is...

In the figure shown, the lower pulley is free to move in a vertical direction only. Block `A` is given a uniform velocity `u` as shown, what is the velocity of block `B` as a function of angle `theta`?

A

`ucostheta`

B

`u/(costheta)`

C

`(u[1+sintheta])/(costheta)`

D

`(u[1+costheta])/(sintheta)`

Text Solution

Verified by Experts

The correct Answer is:
C
Let in a small time `dt`, displacement of `A` is `dx` and displacement of `B` is `dy`. Increase in length `l_(1)=dx`
Increase in the length `l_(2)=dxsintheta-dycostheta`

But net increase in the length in the length should be zero, so
`dx+dxsintheta-dycostheta=0`
`impliesdy=((1+sintheta)dx)/(costheta)`
`=(dy)/(dt)=((1+sintheta)/(costheta)) (dx)/(dt)`
`implies v=((1+sintheta)/(costheta))u`
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