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Question

A square lamina of mass density (σ)=10 kg/m2 and side length 2 m is rotated about an axis passing through one of it’s side as shown in figure. Find the moment of inertia of the lamina about this axis.


A
26.66 kg-m2
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B
16.66 kg-m2
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C
26.33 kg-m2
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D
53.33 kg-m2
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Solution

The correct option is D 53.33 kg-m2
Given, mass density (σ)=10 kg/m2
Side length of square lamina (a) = 2 m

From definition,
mass density (σ)=Mass of square lamina(M)Area of square lamina(A)
Mass of square lamina, (M)=σ×a2
=10×22=40 kg

Moment of inertia of square lamina about an axis passing through one of it’s side, I=Ma23

=40×(2)23
=53.33 kg-m2

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