Question

A uniform disc of radius R is put over another uniform disc of radius $2R$ made of same material having same thickness. The peripheries of the two discs touches each other. Locate the centre of mass of the system taking center of large disc at origin.

Answer 1

m = mass of small disc = $\sigma \left(\pi R^2\right)$

M = mass of large disc = $\sigma \pi {\left(2R\right)}^2=4\sigma \left({\pi R}^2\right)$

center of mass co-ordinate is (x)

$x=\frac{M\times 0+mR}{M+m}=\frac{\sigma \left(\pi R^2\right)R}{4\sigma \left(\pi R^2\right)+\sigma \left(\pi R^2\right)}$

$x=\frac{R}{5}$