Question

A uniform disc or 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. The position of their center of mass is

• A. At $\frac{R}{3}$ from the centre of the bigger disc towards the centre of the smaller disc
• B. At $\frac{R}{5}$ from the centre of the bigger towards the centre of the smaller disc
• C. At $\frac{2R}{5}$ from the centre of the bigger disc towards the centre of the smaller disc
• D. None of these

Answer 1

The correct option is B At $\frac{R}{5}$ from the centre of the bigger towards the centre of the smaller disc

Surface mass density$=\sigma$ (Say)

Mass of $2R$ radius disk$==\sigma \pi (2R{)}^2=4\sigma \pi R^2$ at center $o$.

Mass of $R$ radius disk$=\sigma \pi (R{)}^2$ center $c$

Center of mass $x$$=\frac{0+\sigma \pi \left(R{)}^2\right(R)}{5\left(\sigma \pi \right(R{)}^2)}=\frac{R}{5}$ from $o$ towards $c$.