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  4. 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?

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Q. 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?

WBJEEWBJEE 2015System of Particles and Rotational Motion

Solution:

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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 $'S'', v_{S}=v+\omega R=2 v$
velocity of centre ' $O', v_{0}=v-\omega(0)=v$
Velocity of a point ' $T$ at distance $R$
from $P$ is $V_{T}=\omega R=O v$
Thus possible velocities are $v, 2 v$ and $0 .$