Question

Seven identical discs are arranged in a hexagonal, planar pattern so as to touch each neighbor, 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 center of central disk and normal to plane of all disks?

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

Answer 1

The correct option is D $\frac{55}{2}m{r}^2$


$I=I_0+6I^{\prime }$
$I_0$ is the moment of inertia of central disc and
$I^{\prime }$ is the moment of inertia of rest of each disc about specified axis.

By parallel axes theorem

$I=\frac{m{r}^2}{2}+6(I_{cm}+m{d}^2)$

$=\frac{m{r}^2}{2}+6(\frac{m{r}^2}{2}+m(2r{)}^2)$

$=\frac{m{r}^2}{2}+\frac{6m{r}^2}{2}+24m{r}^2=\frac{55m{r}^2}{2}$


Final Answer: $\left(d\right)$