question_answer

A circular disc rolls on a horizontal floor without slipping and the centre of the disc moves with a uniform velocity v. Which of the following values of the velocity at a point on the rim of the disc can have?

A) \[v\]

B)  \[-\text{ }v\]

C) \[2v\]

D)  Zero

Correct Answer: A

Solution :

Consider the rolling motion of a circular disc as shown in the adjacent diagram. Velocity of   point  of contact  (P) is   velocity of point S, \[{{v}_{S}}=v+\omega R=2v\] velocity of centre\[O,{{v}_{o}}=v-\omega (0)=v\] Velocity of a point T at distance R from P is \[{{V}_{T}}=\omega R=Qv.\] Thus possible velocities are \[v,2v\]and 0.