A disc of radius 20 cm has its center at origin. If a disc of radius 5 cm is cut from it such that its edge touches the …

R = 20 cm, r = 5 cm

Let the mass of big disc is M and the small disc is m.

\(\mathrm{Mass}\mathrm{per}\mathrm{unit}\mathrm{area}=\frac{\mathrm{M}}{\pi {\left(20\right)}^{2}}\\ \mathrm{mass}\mathrm{of}\mathrm{smaller}\mathrm{disc},\mathrm{m}=\frac{\mathrm{M}}{\pi {\left(20\right)}^{2}}\times \pi {\left(5\right)}^{2}=\frac{\mathrm{M}}{16}\)

The coordinates of centre of mass is given as

\({\mathrm{x}}_{\mathrm{cm}}=\frac{\mathrm{M}\times 0-\mathrm{m}\times 15}{\mathrm{M}-\mathrm{m}}=\frac{-\frac{\mathrm{M}}{16}\times 15}{\mathrm{M}-\frac{\mathrm{M}}{16}}=-1\mathrm{cm}\\ {\mathrm{y}}_{\mathrm{cm}}=0\mathrm{cm}\)