Question

One quarter section is cut from a uniform circular disc of radius R. This section has a mass M. It is made to rotate about a line perpendicular to its plane and passing through the centre of the original disc. Its moment of inertia about the axis of rotation is

• A. $\frac{1}{2}M{R}^2$
• B. $\frac{1}{4}M{R}^2$
• C. $\frac{1}{8}M{R}^2$
• D. $\sqrt{2}M{R}^2$

Answer 1

Answer: (A)

Mass of the whole disc = 4M
Moment of inertia of the disc about the given axis
$=\frac{1}{2}(4M)R^2=2M{R}^2$
$\therefore$ Moment of inertia of quarter section of the disc
$=\frac{1}{4}(2M{R}^2)=\frac{1}{2}M{R}^2$