First slide

Vertical circular motion

Question

The tube AC from a quarter circle in a vertical plane. The ball B has an area of crosssection slightly smaller than that of the tube, and can moves without friction through it. B is placed at A and displaced slightly. It will

Easy

A

always be contact with the inner wall of the tube
B

always be in contact with the outer wall of the tube
C

initially be in contact with the inner wall and later with the outer wall
D

initially be in contact with the outer wall and later with the inner wall

Solution

As the ball is moving down the tube, its gravitational P.E. is converted into K.E, speed of the ball gradually increases, centrifugal force (mv²/R) acting on the ball gradually increases. Because of the action of centrifugal force the ball loses contact with the inner wall at some point P. For its journey from p to c, the fall will be in contact with the outer wall of the tube. so option (3) is right.

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