A blocks is dragged on a smooth plane with the help of a rope which moves with a velocity v as shown in the figure. The horizontal velocity of the block is

Options

A. v
B. `v/(sin theta)`
C. `v sin theta`
D. `v/(cos theta)`

Answer

B

Explanation

`x^(2)=y^(2)+d^(2)`
`rArr 2x(dx)/(dt)=2y(dy)/(dt)`
`rArr (dy)/(dt)=(x/y)((dx)/(dt))=v/(sin theta)`
OR
Component of velocity along string must same so
`v_(M) cos theta (90-theta)=vrArr v_(M)=v/(sin theta)`