First slide

Moment of intertia

Question

A circular plate of radius $\frac{R}{2}$ is cut from one edge of thin circular plate of radius R. The moment of inertia of remaining portion about an axis through O perpendclicular to plane of plate is (Where M is the mass of remaining plate)

Difficult

A

$\frac{11 M R^{2}}{24}$
B

$\frac{7 M R^{2}}{12}$
C

$\frac{13 M R^{2}}{24}$
D

$\frac{5 M R^{2}}{7}$

Solution

$I_{R} = I_{1} - I_{2}$
$I_{1} = M I$ of circular solid plate of radius R about O
$I_{2} = M I$ of circular removed plate of radius R/2 about O

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