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Consider two concentric thin wall steel tubes, the larger one closed at the bott

ID: 1856261 • Letter: C

Question

Consider two concentric thin wall steel tubes, the larger one closed at the bottom and the inner one open. The tubes are filled with a fluid. A well fitting cylinderical plug that slides easily is dropped in the inner tube and a well fitting annular ring (doughnet) which slides easily is dropped between the two tubes. The weights of both plugs are the same. After osillating a litle the plugs settle concentrically with one another another as shown. What must be the relationships between the radii of the tubes.

Explanation / Answer

if height of both the plugs are same, then pi*r1^2=pi*(r2^2-r1^2), which implies, r2=1.414r1