Question

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 centre of mass of the system from the centre of large disc.

Answer 1

Let the center of bigger disc be O.

Let the center of smaller disc be P

$OP=R$

Mass of the smaller disc$=m$

Mass of the bigger disc$=4m$, [As area is 4 times]

Now,

Center of mass from O$=\frac{(4m\times 0+m\times R)}{(4m+m)}=\frac{R}{5}$