Question

A body of uniform (in the vertical direction) cross-sectional areaAand mass densityrhofloatsin a liquid of densityrho0(whererho < rho0), and at equilibrium displaces a volumeV. Making useofArchimedes’ principle(that the buoyancy force acting on a partially submerged body isequal to the weight of the displaced liquid), show that the period of small amplitude verticaloscillations about the equilibrium position is

Answer 1

Answer: A body of uniform cross-sectional area A and mass density ? floats in a liquid of density ?0

(where ? < ?0), and at equilibrium displaces a volume V. Making use of Archimedes’ principle

(that the buoyancy force acting on a partially submerged body is equal to the mass of the

displaced liquid), show that the period of small amplitude oscillations about the equilibrium

position is

T= 2
`\pi \sqrt} (V)/(g^(A) )`