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. `v cos theta`
B. `v/(cos theta)`
C. `2v cos theta`
D. `2/(v cos theta)`

Answer

B

Explanation

Here `x^(2)=y^(2)+d^(2)`
So `2x(dx)/(dt)=2y(dy)/(dt)rArr (dy)/(dt)=(x/y)((dx)/(dt))=(x/y)(v)=v/(cos theta)`
OR
Component of velocity along string must be same
so `v_(M) cos theta=vrArr v_(M)=v/(cos theta)`