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Question

As shown in figure, a uniform disc of mass m is rolling without slipping with an angular velocity ω. The portion AB is rough and BC is smooth. If the disc crosses point B, the motion of the disc will be:


A
translational motion only
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B
pure rolling motion
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C
rotational motion only
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D
none of these
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Solution

The correct option is B pure rolling motion
In case of pure rolling, velocities of contact points have to be equal.
i.e VP=VQ
& V=ωR holds always

Since disc is already in a state of pure rolling, V=ωR is maintained. Hence friction won't act on the disc during its journey through the rough portion AB.
Disc will continue pure rolling motion while it travels through smooth portion BC.

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