Q. A rectangular block of mass m and area of cross-section A floats in a liquid of density ρ. If it is given a small vertical displacement from equilibrium it undergoes oscillation with a time period T. Then :
A) T ∝ √ρ
B) T ∝ 1/√A
C) T ∝ 1/ρ
D) T ∝ 1/√m
Explanation
[Solution from source] When the block is pushed down by y, the extra buoyant force is Aρgy, so it behaves like a spring of constant k = Aρg. Hence T = 2π√(m/(Aρg)), which varies as 1/√A (and as 1/√ρ, √m). T is not proportional to √ρ or 1/ρ, and it increases, not decreases, with m. Answer (2).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.