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 R^{2}

(b)I = m R^{2}/2

(c)I = m R^{2}/4

(d)I = m R^{2}/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 I

Where M = Mass of complete disc

_{z}= MR²/2Where 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} $