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)

A test tube weighing 10 g and external diameter 2 cm is floated vertic

1.	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)
Answer» Solution :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 `