A thin square plate of side 3m has mass 5kg. Find the moment of inertia about axis AB as shown in figure.
A
15kg-m2
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B
30kg-m2
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C
45kg-m2
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D
7.5kg-m2
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Solution
The correct option is A15kg-m2 Given, mass of square plate (m)=5kg
Side length of square plate (l)=3m
To find moment of inertia of square plate about AB, let us consider an imaginary square of side 3m adjacent to the given square plate as shown below.
Moment of inertia of complete rectangle about axis AB=ml212
where l is the length of rectangle =6m
and m= mass of rectangle =10kg
IAB for rectangle =10×(6)212=30kg-m2
Therefore, by symmetry IAB for square =30/2=15kg-m2
Alternative method:
MoI of square about an axis passing through geometrical centre and parallel to the sides =ml212
Using parallel axis theorem, MoI about edge AB IAB=ml212+m(l2)2 =ml23 =5×323=15kg-m2