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)

$I=I_{0}+6I'$
$I_{0}$ is the moment of inertia of central disc and $I'$ 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(2 r)^{2}\right] $
$=\frac{m r^{2}}{2}+\frac{6 \,m r^{2}}{2}+24\,m r^{2}=\frac{55\, m r^{2}}{2} $