Question

A weighted glass tube is floating in a liquid with 20 cm of its length immersed. It is pushed down a little and released, calculate the time period of oscillations.

Answer 1

Let B be the point upto which the weighted glass tube is immersed in the liquid such that

l = 20 cm = 0.20 m.

Applying the law of floating,

weight of tube = weight of the liquid displaced = upthrust

∴ mg = (Al)ρg

where m is the mass of the tube, A is cross-sectional area of the tube and ρ is the density of liquid.

m = Alρ = A x 0.20 x p

Let the tube be pushed into the liquid upto point C such that

BC = x

Restoring force = weight of the extra liquid displaced

= Additional upthrust

= - Axρg = - Aρgx