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`?

Options

A. `ucostheta`
B. `u/(costheta)`
C. `(u[1+sintheta])/(costheta)`
D. `(u[1+costheta])/(sintheta)`

Answer

C

Explanation

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`