Let P be the COM of a system of two weights with masses m 1 and m

Question:

Let P be the COM of a system of two weights with masses m₁and m₂separated by a distance d. Prove Archimedes’s Law of the (weightless) Lever: P is the point on a line between the two weights such that m₁L ₁= m₂L₂, where L_jis the distance from mass j to P.