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A disc is rolling, the velocity of its centre of mass is $V_{cm}$, then which one will be correct : -
A
The velocity of highest point is $2V_{cm}$ and point of contact is zero
B
The velocity of highest point is $V_{cm}$ and point of contact is $V_{cm}$
C
The velocity of highest point is $2V_{cm}$ and point of contact is $V_{cm}$
D
The velocity of highest point is $2V_{cm}$ and point of contact is $2V_{cm}$
Detailed Solution
In rolling without slipping, each point has the velocity of the centre of mass $V_{cm}$ plus a rotational velocity $R\omega = V_{cm}$ tangent to the disc.
Top point: both are in the same direction, so $v = V_{cm} + R\omega = 2V_{cm}$.
Point of contact: they are in opposite directions, so $v = V_{cm} - R\omega = 0$ (no slipping).
So the highest point moves with $2V_{cm}$ and the point of contact is momentarily at rest.
Top point: both are in the same direction, so $v = V_{cm} + R\omega = 2V_{cm}$.
Point of contact: they are in opposite directions, so $v = V_{cm} - R\omega = 0$ (no slipping).
So the highest point moves with $2V_{cm}$ and the point of contact is momentarily at rest.