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

Answer 1

Answer: (A)

$\frac{1}{2}MR^2$

Answer 2

Mass of the whole disc = 4M

Moment of inertia of the disc about the given axis

$\, \, \, \, \, \, \, \, \, = \frac{1}{2} (4M) R^2 = 2MR^2$
$\therefore$ Moment of inertia of quarter section of the disc
$\, \, \, \, \, \, \, \, \, = \frac{1}{4} (2M R^2 )= \frac{1}{2}MR^2$