Physics - Fluid Question with Solution | TestHub

Let the block be displaced downwards by a small distance $x$ from its equilibrium position.

The additional volume submerged in the liquid is $Ax$.

The extra buoyant force acting upwards provides the restoring force, which is given by $F=-(\text{additional volume})\times \varrho \times g$

$F=-Ax\varrho g$

Comparing this with the standard equation of simple harmonic motion $F=-kx$, we get the effective force constant $k=A\varrho g$.

The angular frequency of oscillation is $\omega =\sqrt{\frac{k}{m}}=\sqrt{\frac{A\varrho g}{m}}$.

The frequency of oscillation is $f=\frac{\omega }{2\pi }=\frac{1}{2\pi }\sqrt{\frac{A\varrho g}{m}}$.

Answer: $\frac{1}{2\pi }\sqrt{\frac{\text{A}\varrho \text{g}}{\text{m}}}$