A test tube weighing 10 g and external diameter 2 cm is floated vertically in water by placing 10 g of mercury at its bottom. The tube is depressed in water a little and then released. Find the time of oscillation. Take `g=10 ms^(-1)`

Explanation

Total mass of test tube and mercutry,
`m+10+10=20 g=0.02 kg`
Area of cross- section of the test tube tube
`A= pi r^(2)=(22)/(7)xx((1)/(100))^(2)`
Density of water `rho=10kg m^(-3)`
Let the tube be depresed in water by a little distance y and then released.
Spring factor,
`k=(F)/(y)=(A_(y. rho. g))/(y)=A rho g`
`=(22)/(7)Nm^(-1)`
Interia factor, `m=0.02 kg`
`:.T = 2pi sqrt((m)/(k))`
`=2xx(22)/(7)xx sqrt(0.02xx7)/(22)`
`=0.5 `