First slide

Moment of intertia

Question

For the given uniform square lamina ABCD, whose centre is O find the relation between $I_{A C}$ and $I_{E F}$

Moderate

A

$I_{AC} = I_{EF}$
B

$I_{AC} = \sqrt{2} I_{EF}$
C

$\sqrt{2} I_{AC} = I_{EF}$
D

$I_{A C} = 3 I_{EF}$

Solution

Let I_o be the moment of inertia of square lamina ABCD about an axis perpendicular to the plane of the lamina end passing through O. Applying the theorem of perpendicular axes, we get
$2 I_{AC} = I_{0}$
and $2 I_{EF} = I_{0}$
$∴ I_{AC} = I_{EF}$

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