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

Step 1: The time taken for a floating object to rise to the surface depends on the restoring force, which is related to the displaced volume of the body.
Step 2: For a body floating with \(\frac{1}{n}\) of its volume above the surface, the time to return to the surface will scale with the square root of the volume fraction submerged.
Step 3: Therefore, the time \(t\) to return to the surface is proportional to \(\sqrt{n-1}\).