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MHT CET 2023 (11 May, Shift 2) · Wave Basics & Properties of Sound

Wave Basics & Properties of Sound question from MHT CET 2023 (11 May, Shift 2)

Q22MHT CET 2023 · 11 MAY · SHIFT 2Easy

Wave Basics & Properties of Sound

A rectangular block of mass ' $m$ ' and crosssectional area A, floats on a liquid of density ' $\rho$ '. It is given a small vertical displacement from equilibrium, it starts oscillating with frequency ' $n$ ' equal to ( $g =$ acceleration due to gravity)

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Answer: (a)

Pushing the block down by $x$ displaces extra liquid volume $Ax$ , giving extra upthrust $F = -A\rho g\,x$ .
This is SHM with force constant $k = A\rho g$ .
$n = \frac{1}{2\pi}\sqrt{\frac{k}{m}} = \frac{1}{2\pi}\sqrt{\frac{A\rho g}{m}}$
So the answer is (a).

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