First slide

Moment of intertia

Question

The moment of inertia of a uniform semicircular disc of mass M and radius r about a line perpendicular to the plane of the disc through the centre is

Moderate

A

$(1 / 4) {Mr}^{2}$
B

$(2/5) {Mr}^{2}$
C

$(1 / 2) {Mr}^{2}$
D

Mr²

Solution

We know that the moment of inertia of a circular disc about an axis perpendicular to the plane of disc and passing through centre is $(1/2) {Mr}^{2} .$
For semi-circular disc
$\begin{array}{l} I = \frac{1}{2} [\frac{1}{2} (2 M) r^{2}] \\ = \frac{1}{2} {Mr}^{2} \end{array}$

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