A solid sphere A of radius R and mass M is attached at a point to a smaller solid sphere B of radius r<R and mass m<M. Assume that the line joining…

A solid sphere $\displaystyle A$ of radius R and mass M is attached at a point to a smaller solid sphere $\displaystyle B$ of radius $\displaystyle \mathrm{r}<\mathrm{R}$ and mass $\displaystyle \mathrm{m}<\mathrm{M}$. Assume that the line joining their centres lies along the horizontal. The moment of inertia of the system calculated about a vertical axis passing through the centre of $\displaystyle A$ is $\displaystyle I_A$ and that calculated about a vertical axis passing through the centre of $\displaystyle B$ is $\displaystyle I_B$. The difference $\displaystyle I_A-I_B$ is :