Q: Moment of inertia of a quarter disc having mass m and radius R about axis passing through centre of disc and perpendicular to plane is
(a)I = m R2
(b)I = m R2/2
(c)I = m R2/4
(d)I = m R2/8
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Solution: Moment of inertia (I) about z axis of a disc passing through centre of mass and perpendicular to the plane of disc is Iz = MR²/2
Where M = Mass of complete disc
Where M = Mass of complete disc
Since each quarter will have same moment of inertia (I)
$ \displaystyle 4I = \frac{M R^2}{2} $
$ \displaystyle I = \frac{M R^2}{8} $
Since M = 4 m
where m = mass of each quarter of disc.
$\displaystyle I = \frac{4m \times R^2}{8} $
$ \displaystyle I = \frac{m R^2}{2} $