Question

Four similar point masses ( $m$ each) are symmetrically placed on the circumference of a disc of mass $M$ and radius $R$ . Moment of inertia of the system about an axis passing through centre $O$ and perpendicular to the plane of the disc will be

• A. $MR^{2}+4mR^{2}$
• B. $MR^{2}+\frac{8}{5}mR^{2}$
• C. $mR^{2}+8MR^{2}$
• D. $\frac{M R^{2}}{2}+4mR^{2}$

Answer 1

Answer: (D)

Moment of inertia of the disc passing through the centre perpendicular to the plane is given by, $I_{D}=\frac{M R^{2}}{2}$ .
Each point mass is separated by a distance $R$ from the axis, so moment of inertia of all the point masses is, $I_{p}=4mR^{2}$
Total moment of inertia of the system about the axis is, $I=I_{D}+I_{p}$
$\Rightarrow I=\frac{M R^{2}}{2}+4mR^{2}$