A liquid rotates as a rigid body with constant angular speed ω about a vertical axis. Which statements are correct?
Select all that apply

Question

A liquid rotates as a rigid body with constant angular speed ω about a vertical axis. Which statements are correct?

G1 Physics · Accepted Answer

For rigid-body rotation, radial equilibrium gives dP/dr = ρω²r. Therefore pressure increases with r. Vertical equilibrium gives dP/dz = −ρg. On the free surface pressure is constant. Combining the two relations gives z = constant + ω²r²/(2g), which is a paraboloid of revolution. Thus the surface is lowest at the axis and rises toward the rim. Integrating the radial pressure gradient at the same height gives P₂−P₁ = ρω²(r₂²−r₁²)/2. Therefore all four statements are correct.