A rectangular block of mas $M$ and cross-sectional area $A$ floats on a liquid of density $\rho$. It is…
A rectangular block of mas $M$ and cross-sectional area $A$ floats on a liquid of density $\rho$. It is given a small vertical displacement from equilibrium; it starts oscillating with frequency $n$ then
$n \propto \sqrt{A}$
$n \propto A^3$
$n \propto A$
$n \propto A^2$
Solution
$\begin{aligned} & F_{\text {restoring }}=(-\rho(A x) g)=m a \\ & \Rightarrow a-\left(g \frac{\rho A}{m}\right) x \\ & \Rightarrow \omega=\sqrt{\frac{\rho A g}{m}}=2 \pi n \\ & \Rightarrow n \propto \sqrt{A}\end{aligned}$