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Question

A rectangular plate of mass m=3 kg having sides a=4 m and b=2 m is placed on XY plane as shown in figure. Find the moment of inertia of rectangular plate about an axis passing through the point O and perpendicular to its plane.

A
5 kg-m2
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B
4 kg-m2
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C
1 kg-m2
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D
3 kg-m2
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Solution

The correct option is A 5 kg-m2

Given:
a=4 m
b=2 m
Mass of rectangular plate m=3 kg
Ix and Iy be the moment of inertia of rectangular plate about an axis passing through the point O in the plane of plate.
So, we have
Ix=ma212=3×4212=4 kg-m2
Iy=mb212=3×2212=1 kg-m2

Applying perpendicular axis theorem
Iz=Ix+Iy
=(1+4) kg-m2
=5 kg-m2
So, moment of inertia of rectangular plate about an axis passing through the point O and perpendicular to its plane is 5 kg-m2

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