From a circular disc of radius R and mass 9M, a small disc of mas… - Vidyadip

MCQ

From a circular disc of radius $R$ and mass $9M$, a small disc of mass $M$ and radius $\frac{R}{3}$ is removed concentrically. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through its centre is

A
$M{R^2}$
B
$4M{R^2}$
C
$\frac{4}{9}\,M{R^2}$
✓
$\frac{40}{9}\,M{R^2}$

✓

Answer

Correct option: D.

$\frac{40}{9}\,M{R^2}$

d
$\mathrm{I}_{\mathrm{net}}=\mathrm{I}_{\mathrm{disc}}-\mathrm{I}_{\mathrm{removed}}$

$=\frac{1}{2}(9 M) R^{2}-\frac{1}{2} M\left(\frac{R}{3}\right)^{2}=\frac{40}{9} \,M R^{2}$

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