A uniform disc of radius R is put over another uniform disc of radius 2R of same thickness and density. The peripheries of the two discs touch each other. The position of their center of mass is:
Given,
Smaller disc radius, =R
Larger disc radius, =2R
Density of disc =ρ
Thickness of disc=t
Mass of larger disc and smaller disc, mL & ms
Assume center of mass at distance x, from center of larger disc toward center of smaller disc.
From, formula of Center of Mass
ms×R+mL×0=(ms+mL)×x
x=ms×Rms+mL=ρ(πR2t)×Rρ(πR2t)+ρ[π(2R)2t]=R5
center of mass at distance R5, from center of larger disc toward center of smaller disc