Question

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

• A. Always be in 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 1

Answer: (C)

When the ball is released, we know that after an anglular displacement $\theta=\cos ^{-1}(-2 / 3)$ ball leaves contact with the inner wall of the tube and get in contact with the outer wall of the tube hence option (C) is correct.