# Upward Lifting force on a Cone!

**Classical Mechanics**Level 5

A conical cup of height \(b\), semi-vertical angle \(\alpha\) rests open end down on a flat surface as shown. The cup is filled to height \(H\) with liquid of density \(\rho\) and a small hole is punched at the apex of the cone. The upward lifting force on the cup is \(F= \pi \rho g [bH^2 - \frac{H^3}{n}] \tan^2 \alpha \) , then '\(n\)' is