From a uniform square plate of a side a and mass m, a square portion defg of side a/2 is removed. then, the moment of inertia of remaining portion about the axis ab is?
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Explanation:
MI of a square plate about an an edge in the plane of the plate and passing through center and parallel to an edge is:I=
12
ma
2
using perpendicular axis theorem.
Using parallel axis theorem, MI about an edge is: I=
12
ma
2
+m(
2
a
)
2
=
3
ma
2
I
AB
=I
1
+I
2
+I
3
=
3
(m/3)(a/2)
2
+
3
(m/3)(a/2)
2
+[
12
(m/3)(a/2)
2
+(m/3)(
4
3a
)
2
]
=
16
3
ma
2
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