Question

# The moment of inertia of a thin square plate ABCD, of uniform thickness about an axis passing through the centre O and perpendicular to the plane of the plate is (where $$I_1, I_2, I_3 \ and \ I_4$$ are respectively moments of inertia about axis 1,2,3, and 4 which are in the plane of the plate)

A
I1+I2
B
I3+I4
C
I1+I3
D
I1+I2+I3+I4

Solution

## The correct options are A $$I_1 +I_2$$ B $$I_3 +I_4$$ C $$I_1 +I_3$$$$\begin{array}{l}\text { We know that moment of inertia of a square } \\\text { blate about any axis parallel to its fau } \\\text { passing through is centre is always equal } \\\Rightarrow I_{1}=I_{2}=I_{3}=I_{4} \\\Rightarrow \text { For an axis perpendicular to the face of } \\\text { plate- } \\\text { By perpendicular axis theorem- } \\\qquad I_{\perp}=I_{1}+I_{2}=I_{3}+I_{4}=I_{1}+I_{3} \\\text { Henu, option }(a),(b),(c)\text { are correct. }\end{array}$$Physics

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