In a rectangle ABCD (BC = 2AB), the moment of inertia is minimum along axis through 

Concept:

Moment of inertia:

• The moment of inertia of a rigid body about a fixed axis is defined as the sum of the product of the masses of the particles constituting the body and the square of their respective distances from the axis of the rotation.
• The moment of inertia of a particle is

⇒ I mr2

Where r = the perpendicular distance of the particle from the rotational axis.

Explanation:

Given that, BC = 2AB

\( {I_{BC}} = \frac{{M{{(AB)}^2}}}{3} = \frac{{m{a^2}}}{3}\)

\( i.e\;AB = a = \frac{{BC}}{2} \)

\( Moment\:of\:inertia\:at\:AB,{I_{AB}} = \frac{{m{{(BC)}^2}}}{3} = \frac{{M{{(2a)}^2}}}{3} = \frac{{4m{a^2}}}{3} \)

\( Moment\:of\:inertia\:at\:HF,{I_{HF}} = \frac{{m{{(AB)}^2}}}{{12}} = \frac{{m{a^2}}}{{12}} \)

\(Moment\:of\:inertia\:at\:EG,{I_{EG}} = \frac{{m(BC)}}{{12}} = \frac{{m{a^2}}}{{12}} \)

The moment of inertia is minimum about EG because mass distribution is at the minimum distance from EG