First slide

Moment of intertia

Question

The diagram shows a uniform disc of mass M and radius 'a'. If the moment of inertia of the disc about the axis XY is I, its moment of inertia about an axis through0and perpendicular to the plane of the disc is :

Moderate

A

$\frac{4}{3} {Ma}^{2}$
B

$I + \frac{1}{4} {Ma}^{2}$
C

2I
D

$\frac{I}{2}$

Solution

$\begin{array}{l} I = \frac{{Ma}^{2}}{4} + \frac{{Ma}^{2}}{4} = \frac{{Ma}^{2}}{2} \\ I_{O} = I_{C} + M {(\frac{a}{2} \sqrt{2})}^{2} = \frac{{Ma}^{2}}{2} + \frac{{Ma}^{2}}{2} = {Ma}^{2} = 2 I \end{array}$

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