An open ended test tube which contains sea water is put into a uniform circular motion on the horizontal plane as shown below. The height of the water level in the tube is denoted as h and the surface of the water is at a distance r0 from the center of the circular path.
a) Find the pressure in the water as a function of distance from the center point O. Hence, the answer will include the atmospheric pressure P0 , water density ρ and the angular speed of the test tube ω.
b) Find the angular speed which would cause the pressure at the bottom of the test tube to be equal to the pressure at a depth of H from the surface of a sea. If H=100m, r0=50cm and h=5cm, how fast the test tube should be rotated to provide the desired pressure at the bottom of the test tube?