A uniform disc of radius R is put over another uniform disc of radius 2R of the same thickness and density. The peripheries of the two discs’ touch each other. Locate the center of mass of the system.

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Let the density (mass/volume) of the both the discs be ‘ρ’ and thickness ‘t’.


Then, mass of the bigger disc m1 = ϖ(2R)2


And mass of the smaller disc m2 = ϖR2


Position of center of mass of the bigger disc (x1, y1) = (0,0)


Position of center of mass of the smaller disc (x2, y2) = (R,0)


Considering point O as the origin,


The position of the center of mass (x, y)






The center of mass of the system is at R/5 distance from the center of the bigger disc towards the center of the smaller disc.


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