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.

A weighted glass tube is floated in a liquid with 20 cm of its length

1.	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.
Answer» Solution :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 cm0.20 m` `T=2pisqrt((0.2)/(9.8))` `= 2 xx3.14 sqrt((0.2)/(9.8))=0.897s`