A disc is rolling (without slipping) on a horizontal surface. `C` is its center and `Q` and `P` are two points equidistant from `C`. Let `V_(P), V_(Q)` and `V_(C)` be the magnitude of velocities of points `P, Q` and `C` respectively, then
.

Options

A. `v_(Q) gt v_(C) gt v_(P)`
B. `v_(Q) lt v_(C) lt v_(P)`
C. `v_(Q) = v_(P)`, `v_(C) = v_(P)`
D. `v_(Q) lt v_(C) gt v_(P)`

Explanation

`v_(C)=v`
`P :`
`v_(P)=sqrt(v^(2)+(romega)^(2)+2xxvxxromega cos(90+theta))`
`Q :`
`v_(Q)=sqrt(v^(2)+(romega)^(2)+2xxvxxromega costheta)`
`v_(Q) gt v_(C) gt v_(P)`
OR
Assuming motion as the case of pure rotation about the point of contact
`v_(C)=Romega, v_(Q)=r_(2)omega, v_(P)=r_(1)omega`
`v_(Q) gt v_(C) gt v_(P)`