The Ball in Liquid columns Coulumns

Classical Mechanics Level 4

A heavy cylinder of radius \(R\) lies in equilibrium on a smooth surface, separating two liquids of densities \(\rho_l\) on the left and \(\rho_r\) on the right, with \(\rho_r > \rho_l.\)

If the height of the liquid on the right is \(R,\) what is the height \(h\) of the liquid on the left in terms of \(R?\)

Neglect the surface tensions of the liquids.

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