Question

Seven identical disc are arranged in a hexagonal, planar pattern so as to touch each neighbour, as shown in the figure. Each disc has mass $m$ and radius $r$. What is the moment of inertia of the system of seven disks about an axis passing through the centre of central disk and normal to plane of all disks?

• A. $\frac{7}{2}m{r}^2$
• B. $\frac{13}{2}m{r}^2$
• C. $\frac{29}{2}m{r}^2$
• D. $\frac{55}{2}m{r}^2$

Answer 1

Answer: (D)

$I=I_0+6I^{\prime }$
$I_0$ is the moment of inertia of central disc and $I^{\prime }$ is moment of inertia of rest of the each disc about specified axis.
By parallel axes theorem
$I=\frac{m{r}^2}{2}+6\left(I_{cm}+m{d}^2\right)=\frac{m{r}^2}{2}+6\left[\frac{m{r}^2}{2}+m(2r{)}^2\right]$
$=\frac{m{r}^2}{2}+\frac{6m{r}^2}{2}+24m{r}^2=\frac{55m{r}^2}{2}$