Q. A cylindrical cork of uniform density floats in a liquid of density ρ₁. 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 ρ₂, then the similar oscillation has time period 2T. The value of ρ₂/ρ₁ is:
A) 1/4
B) 4
C) 2
D) 1/2
Explanation
[Solution from source] For a floating cylinder the restoring force per unit depression is ρAg, so $T=2\pi\sqrt{m/(\rho Ag)}\propto1/\sqrt\rho$. Doubling T requires $\rho_2=\rho_1/4$. Answer (1).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.