Question

Find the moment of inertia of a pair of spheres, each having a mass $m$ and radius $r$, kept in contact about the tangent passing through the point of contact.

Answer 1

Moment of Inertia of one sphere body about its axis is

$I=\frac{2}{5}m{r}^2$

Now, $MoI$ of first axis parallel to other axis

$I^{\prime }=I+m{r}^2$

$=\frac{2}{5}m{r}^2+m{r}^2=\frac{7}{5}m{r}^2$

Therefore, the Moment of inertia of the pair of spheres is:

$I=I_1+I_2$

$=\frac{7}{5}m{r}^2+\frac{7}{5}m{r}^2$

$=\frac{14}{5}m{r}^2$