A sprayer consists of four bent pipes of length 2a for each pipe. The pipes can freely rotate about point O without friction.An ideal fluid of mass density ρ flows into the sprayer through point O from a large tank of pressure P (assume it's much larger than atmospheric pressure).
After a long time, the sprayer reaches a constant angular velocity, ω. Ignore gravity, energy lost, and turbulence of fluid.
Calculate ω!


Click here to read the solution.

A solid ball with radius r and mass m is located inside an opened wide tank filled with water. The ball has the same density with water.
Calculate work required to get the ball out from the water!Ignore viscosity and surface tension. Gravity acceleration is g.

(Don't use straight-forward method, this problem doesn't need integration at all)

A rectangle block with dimension a*b*c floats on water. The block's mass density is a half of water density, so only half part of the block inside the water. See picture below.Find the minimum value of a/b in order to make it stable, if it's rotated slightly around axis O!

(Hint: if you understand the concept, it would be much easier)