A disc of radius R is cut out from a larger disc of radius 2R in such a way that the edge of the hole touches the edge of the disc. Locate the center of mass of the residual disc.

Question

Philoid · Accepted Answer

Let the density (mass/volume) of the both the discs be ‘ρ’ and thickness ‘t’.

Then, mass of the bigger disc m₁ = ϖ(2R)²tρ

And mass of the disc cut out m₂ = ϖR²tρ

Position of center of mass of the bigger disc (x₁, y₁) = (0,0)

Position of center of mass of the disc cut out (x₂, y₂) = (R,0)

Considering point O as the origin, Position of the new center of mass (x, y)

∴ The center of mass of the residual disc is at R/3 distance from the center of the bigger disc away the center of the hole.