A disc of radius R is rolling (without slipping) on a frictionless surface as shown in figure. C is it's centre and Q and P are two points equidistant from C. Let vP,vQ and vC be the magnitudes of velocities of points P, Q and C respectively, then
The correct option is CvQ>vC>vP
Points P and Q are equidistant from C, then CQ=CP=r Let ω be the angular speed of disc. For pure rolling, v=Rω, where v is the translational velocity of COM of the disc. ⇒Net velocity at any point on the disc will be due to vector sum of translational velocity and tangential velocity due to rotational motion.
⇒→vQ will be greater in magnitude compared to →vP, since taking resultant of velocities, θ<90∘,cosθis+ve hence component vectors will add up together at point Q ⇒ At point P, angle between velocity vectors is θ>90∘,cosθis−ve so component vectors will get substracted at point P to give resultant →vP. and at point C, |→vC|=v.