Question

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 the velocity at a point on the rim of the disc can have?

• A. v
• B. -v
• C. 2 v
• D. Zero

Answer 1

Answer: (A), (C), (D)

Consider the rolling motion of a circular disc as shown in the adjacent diagram. Velocity of point of contact (P) is
$v_P=v-\omega R=v-v=0$
$[\because v=\omega R]$
velocity of point ${}^{\prime }{S}^{\prime \prime },v_S=v+\omega R=2v$
velocity of centre ' $O^{\prime },v_0=v-\omega (0)=v$
Velocity of a point ' $T$ at distance $R$
from $P$ is $V_T=\omega R=Ov$
Thus possible velocities are $v,2v$ and $0.$