A weighted glass tube is floated in a liquid with 20 cm of its length immersed. It is pushed down through a certain distance and then released. Compute the time period of its vibration.

Explanation

Height to which the tube is immersed in the liquid
= h=20 cm
Let the mass of the tube bem and the density of the liquid bep. The tube floats when the weight of the tube equals the upthrust (see Fig.)
`mg = 20 xx A xxrhog`
`m = 20 xx Arho` where A is the area of cross-section of the tube.
Let y be the depth through which the tube is pushed into the liquid.
Restoring force on the tube = `yArhog`
Acceleration of the tube `=( yArhog)/(20 Arho)`
= `(yg)/20`

The acceleration is proportional to the displacement. So the motion of the tube is shm. The period of oscillation is given by
`T=2pisqrt(("Displacement")/("Acceleration"))`
`= 2pisqrt(y/(yg//20))`
`y = 20 cm 0.20 m`
`T=2pisqrt((0.2)/(9.8))`
`= 2 xx3.14 sqrt((0.2)/(9.8))=0.897s`