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
5kg-m2
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B
4kg-m2
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C
1kg-m2
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D
3kg-m2
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Solution
The correct option is A5kg-m2
Given: a=4m b=2m 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=1kg-m2
Applying perpendicular axis theorem Iz=Ix+Iy =(1+4) kg-m2 =5kg-m2 So, moment of inertia of rectangular plate about an axis passing through the point ′O′ and perpendicular to its plane is 5kg-m2