In the arrangement shown in the fig. the ends P and Q
color
of a string are being moved downwards with a speed of v each. The pulleys are fixed. The mass M moves upwards with a speed of :

Options

A. `v/(costheta)`
B. `(2v)/(costheta)`
C. `vcostheta`
D. `2vcostheta`

Answer

A

Explanation

As P and Q move downwards with same velocity, the mass M moves upwards and leng th of string I decreases at the rate of Vm`s^(-1)`

Here `l^(2) =y^(2) + a^(2)`
diff. w.r.t time,`:. 2l (dl)/(dt)=2y dy/dt +0`
since `(dl)/(dt)=v`
`:. (dy)/(dt)=1/y v`
Thus velocity of block `M=v/(costheta)`