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Q.

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

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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

answer is C.

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Detailed 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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