Determine the minimum weight W of the cylinder that will prevent the cylinder from tipping over.

Question

A smooth hollow cylinder of radius r open at both ends rests on a smooth horizontal plane. Two smooth spheres of weights W₁ and W₂ and radii r₁ and r₂ respectively are placed inside the cylinder, with the larger sphere (radius r₂) resisting on the horizontal plane as shown in Fig. 1.

Determine the minimum weight W of the cylinder that will prevent the cylinder from tipping over.

Answer 1

Reaction acting R₁and R₂ are