Question

A uniform disc of diameter R/2 is put over another uniform disc of diameter R of a same thickness and density.the peripheries of the 2 discs touch each other. the centre of mass of system from centre of big disc is
1)R/10
2)R/20
3)9R/10
4)11R/10

Answer 1

Let the center of the larger disc be at origin.
CM = Center of area
= [π(R/2)^2 * 0 + π(R/4)^2 * (R/4)] / [π(R/2)^2 + π(R/4)^2]
= (πR^3/64) / (5πR^2/16)
= R/20 cm from the center of the larger disc towards the center of the smaller disc.