A disc having radius `R` is rolling without slipping on a horizontal (`x-z`) plane. Centre of the disc has a velocity `v` and acceleration `a` as shown.
Speed of point `P` having coordinates `(x,y)` is

Options

A. `(vsqrt(x^(2)+y^(2)))/(R`
B. `(vsqrt(x^(2)+(y+R)^(2)))/R`
C. `(vsqrt(v^(2)+(y-R)^(2)))/R`
D. none of these

Answer

B

Explanation

`omega=v/R`, Distance of `P` from origin
`r=sqrt(x^(2)+y^(2))`
origin is instantaneous centre of rotatio. So,
`v_(P)=omegar=(vsqrt(x^(2)+y^(2)))/R`