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MHT CET 2021 (20 Sep, Shift 2) · Archimedes' Principle & Floatation

Archimedes' Principle & Floatation question from MHT CET 2021 (20 Sep, Shift 2)

Q13MHT CET 2021 · 20 SEP · SHIFT 2Difficult

Archimedes' Principle & Floatation

A body of density $V$ is dropped from (at rest) height ' $h$ ' into a lake of density ' $\delta$ ' $(\delta > \rho)$ . The maximum depth to which the body sinks before returning to float on the surface is [Neglect all dissipative forces]

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Answer: (d)

Speed at the lake surface: $v^2 = 2gh$ .
In water, net upward force $= V(\delta - \rho)g$ , so retardation $a = \dfrac{(\delta - \rho)g}{\rho}$ .
Maximum depth $= \dfrac{v^2}{2a} = \dfrac{h\rho}{\delta - \rho}$
So the answer is (d).

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