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  4. Moment of inertia of a uniform circular disc about a diameter is I. Its moment of inertia about an axis perpendicular to its plane and passing through a point on its rim will be

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Q. Moment of inertia of a uniform circular disc about a diameter is $I$. Its moment of inertia about an axis perpendicular to its plane and passing through a point on its rim will be

AIPMTAIPMT 1990System of Particles and Rotational Motion

Solution:

Moment of inertia of uniform circular disc about diameter $=I$
According to theorem of perpendicular axes.
Moment of inertia of disc about axis $=2 I=\frac{1}{2} m r^{2}$
Applying theorem of parallel axes
Moment of inertia of disc about the given axis
$=2 I+m r^{2}=2 I+4 I=6 I$.