A uniform disc of radius R/2 is put over another uniform disc of radius R of same thickness and density. The peripheries of the two disc touch each other. The centre of mass of the system is from centre of big disc
Let σ is mass per unit area.
Mass of disc of radius R is M1=σ×A1=σ×πR2
Mass of disc of radius R/2 is M2=σ×A2=σ×πR24
Let the centre of the disc of radius R be at the origin. The arrangement is shown in the figure below.
We know that,
Centre of mass = xcm=M1x1+M2x2M1+M2
⇒xcm=σπR2×0+σπR24×R2σ×πR2+σ×πR24
⇒xcm=R10
Hence, xcm=R10 right to the centre of the big disc.