Question

A body floats with \(\frac{1}{n}\) of its volume keeping outside of water. If the body has been taken to height \(h\) inside water and released, it will come to the surface after time \(t\). Then:

• A. \(t \propto \sqrt{n}\)
• B. \(t \propto n\)
• C. \(t \propto \sqrt{n+1}\)
• D. \(t \propto \sqrt{n-1}\)

Hint:

For buoyant bodies, the time to return to the surface is proportional to the square root of the submerged volume ratio.

Answer 1

The Correct Option is A

Phase 1: An object's ascent time is influenced by the restoring force, which depends on the displaced volume.
Phase 2: If \(\frac{1}{n}\) of the object's volume is above the surface, the return time scales with the square root of the submerged fraction.
Phase 3: Consequently, the return time \(t\) is proportional to \(\sqrt{n-1}\).