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Question

What is the moment of inertia of a square sheet of slide and mass per unit area μ unit area μ about an axis. Passing through the center and perpendicular to its plane:

A
μl212
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B
μl26
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C
μl412
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D
μl46
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Solution

The correct option is D μl46

Given that,

Side = l

Mass per unit area = μ

Total mass M=μl2

Now, the moment of inertia is

I=MR212

By perpendicular axis theorem

I=Ix+Iy

I=2Ix

I=2×μl2×l212

I=μl46

Hence, the moment of inertia of a square sheet is μl46


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