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

Options

A. 2Ucos`theta`
B. U/cos`theta`
C. 2U/cos`theta`
D. Ucos`theta`

Answer

B

Explanation

In the right angle `Lambda PQR`
`l^(2) =c^(2)+y^(2)`
Differentiating this equation with respect to time, we get
`2l(dl)/(dt) =0+2y(dy)/(dt)` or `((-dy)/(dt))=(l)/(y) ((-dl)/(dt))`
Here ` -(dy)/(dt)=u_(M),(l)/(y)=(1)/(cos theta)` and `-dl//dt =U`
Hence `u_(M) =(U)/(cos theta)`
`:.` the corrent option is (b)