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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