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Question

A ball is given a velocity v and angular velocity such that the ball rolls purely on a plank whose upper surface is rough enough to prevent slipping but lower surface in contact with the ground is smooth. No other force is acting on system.

A
The plank will recoil back.
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B
The plank will also move forward but with a lesser velocity than that of the ball.
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C
The plank will also move forward but with a greater velocity that that of the ball.
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D
The plank will remain at rest.
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Solution

The correct option is D The plank will remain at rest.
Velocity of point B should be zero w.r.t the plank as the ball rolls purely on the plank. There is no need of friction force to rotate the ball as the ball will exhibit rotational motion without sliding on its own inertia. Thus there is no reaction force on the plank and hence it will remain at rest.
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