Question

Seven identical circular planar disks, each of mass $M$ and radius $R$ are welded symmetrically as shown. The moment of inertia of the arrangement about the axis normal to the plane and passing through the point $P$ is -

• A. $\frac{19}{2}M{R}^2$
• B. $\frac{55}{2}M{R}^2$
• C. $\frac{73}{2}M{R}^2$
• D. $\frac{181}{2}M{R}^2$

Answer 1

Answer: (D)

$I_0=\frac{M{R}^2}{2}+6\left(\frac{M{R}^2}{2}+M{\left(2R\right)}^2\right)$
$I_P=I_o+7M{\left(3R\right)}^2$
$=\frac{181}{2}M{R}^2$