Find velocity of piston A in the given situation if angular velocity of wheel of radius R is `omega` (constant) in the clockwise sense (O is fixed point)

Options

A. `(xRomegasintheta)/(Rcostheta+x)`
B. `(x^(2)omegasintheta)/(Rcostheta-x)`
C. `(xRomegasintheta)/(Rcostheta-x)`
D. `(R^(2)omegasintheta)/(Rcostheta-x)`

Answer

C

Explanation

`costheta=(x^(2)+R^(2)-L^(2))/(2xR)implies2xRcostheta=x^(2)+R^(2)+L^(2)`
`2R{-xsintheta((d theta)/(dt))+costheta((dx)/(dt))}=2x(dx)/(dt)`
`xv=Rvcostheta-Rxomegasintheta`
`impliesv=((xRomegasintheta)/(Rcostheta-x))`