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Question

A two dimensional lamina of arbitrary shape is placed in x−y plane as shown in the figure. MOI of lamina about x and y axes are Ix=6 kg-m2 and Iy=4 kg-m2 respectively. If point of intersection (O) of the axes does not lies on lamina, then the MOI of lamina about z axis i.e. (Iz) will be

A
6 kg-m2
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B
4 kg-m2
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C
8 kg-m2
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D
10 kg-m2
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Solution

The correct option is D 10 kg-m2

Given, Ix=6 kg-m2 and Iy=4 kg-m2
As we know,
For using Perpendicular axis theorem, point of intersection of the three axis need not be COM, it can be any point in the plane of body which lies on the body or even outside it.

Using Perpendicular axis theorem we get
Iz=Ix+Iy =(6+4) kg-m2 =10 kg-m2

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