Q 11-13-001NEETNEET 2026Top questionMedium
A cylindrical cork of uniform density floats in a liquid of density $\rho_1$. If the cork is depressed slightly and released, it oscillates harmonically with time period $T$. If the same cork floats in another liquid of density $\rho_2$, then the similar oscillation has time period $2T$. The value of $\rho_2/\rho_1$ is :
Answer: (D) $1/4$
For a cork of mass $m$ and cross-section area $A$, pushing it down by $y$ adds a buoyant restoring force $\rho A g y$. So
$$k = \rho A g, \qquad T = 2\pi\sqrt{\frac{m}{\rho A g}} \;\Rightarrow\; T \propto \frac{1}{\sqrt{\rho}}$$
$$\frac{T_2}{T_1} = \sqrt{\frac{\rho_1}{\rho_2}} = 2 \;\Rightarrow\; \frac{\rho_2}{\rho_1} = \frac{1}{4}$$
Solution by Sreeraj P, M.Sc Physics