A liquid rotates as a rigid body with angular speed ω. The difference in free-surface height between the axis and radius R is ω²R²/(ng). Find n.

Question

G1 Physics · Accepted Answer

For rigid-body rotation, dz/dr=ω²r/g. Integrating from 0 to R gives Δh=∫₀ᴿ(ω²r/g)dr=ω²R²/(2g). Hence n=2.