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(x^(2)-(y-R)^(2)))/R`
D. none

Answer

A

Explanation

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