A uniform disc of radius $R$ is put over another uniform disc of radius $2 R$ of same thickness and density. The peripheries of the two discs touch each other. FInd the position of their centre of mass.

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Solution

Let density be $σ$ and thickness be $d$
Mass of smaller disk (m), m= $m = σ (π R^{2} d)$ from center c
Mass of bigger disk (M), M= $M = σ (π ({2 R}^{2}) d)$ from center O.
$X_{c e n t e r o f m a s s} = \frac{M \times 0 + m (R)}{M + m}$
= $\frac{σ (π R^{2} d) R}{5 σ π R^{2} d} = \frac{R}{5}$

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