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) $1/4$
Concept. Pushing a floating cork down by $y$ adds a buoyant restoring force $\rho Agy$, so $k = \rho Ag$ and $T = 2\pi\sqrt{\dfrac{m}{\rho Ag}} \propto \dfrac{1}{\sqrt\rho}$.
Step 1. Ratio of periods.
$$\frac{T_2}{T_1} = \sqrt{\frac{\rho_1}{\rho_2}} = 2$$
Step 2. Solve. $\dfrac{\rho_2}{\rho_1} = \dfrac14$.
Answer. $1/4$ (Option D).
Solution by Sreeraj P, M.Sc Physics