Question

A circle of radius R is cut from a uniform thin sheet of metal. A circular hole of radius R/2 is now cut out of the circle, with the hole tangent to the rim. Find the distance of centre of mass from the center of the original uncut circle to the CM.

Answer 1

let origin be the centre of metal disc

$0=[M1X1+M2X2][M1+M2]$

mass of disc of diameter $R=\frac{M}{4}$

$0=\frac{[\frac{3m}{4}X+(M/4\left)\right(R/2\left)\right]}{[3M/4+M/4]}$

$X=\frac{-R}{6}$