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MHT CET 2023 (11 May, Shift 1) · Archimedes' Principle & Floatation

Archimedes' Principle & Floatation question from MHT CET 2023 (11 May, Shift 1)

Q12MHT CET 2023 · 11 MAY · SHIFT 1Difficult

Archimedes' Principle & Floatation

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

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Answer: (a)

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

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