Question

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

• A. $\frac{1}{4}Mr^{2}$
• B. $\frac{2}{5}Mr^{2}$
• C. $Mr^{2}$
• D. $\frac{1}{2}Mr^{2}$

Answer 1

Answer: (D)

The mass of complete (circular) disc is
The moment of inertia of disc about the given axis is
$I=\frac{2\,Mr^{2}}{2} =Mr^{2}$
Let, the moment of inertia of semicircular disc is $I_{1}$ The disc may be assumed as combination of two semicircular parts.
Thus, $I_{1}=I-I_{1}$
$\therefore I_{1}=\frac{I}{2}=\frac{Mr^{2}}{2}$