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

Options

A. `2Ucostheta`
B. `Ucostheta`
C. `(2U)/(costheta)`
D. `(U)/(costheta)`

Answer

D

Explanation

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)` .