A uniform disc of radius R is placed upon another uniform disc of radius 2R having the same thickness and density. The edges of the two discs touch one another. Determine the location of the centre of mass of the system.

Step-by-step solution

Let the mass of the smaller disc be m . Since both discs have the same thickness and density, their masses are proportional to their areas. Area of the smaller disc = R^2 Area of the larger disc = (2R)^2 = 4 R^2 Mass of the larger disc, M = 4m Let the center of the larger disc be at the origin (0,0) . Since the smaller disc is placed upon the larger disc and their edges touch, the smaller disc is internally tangent to the larger disc. The distance between their centers is 2R - R = R . Let the center of the smaller