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

Answer 1

Answer: (D)

$\frac{181}{2} MR^2$

Answer 2

$I_{0} =\frac{MR^{2} }{2} + 6 \left( \frac{MR^{2}}{2} + M\left(2R\right)^{2}\right)$ $I_{P} = I_{o} + 7 M\left(3R\right)^{2}$ $= \frac{181}{2}MR^{2}$