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Question

A square plate lies in the xy plane with its centre at the origin and its edges parallel to the x and y axes. Its moments of inertia about the x,y and z axes are Ix, Iy and Iz respectively, and about a diagonal it is ID. Then:

A
Ix=Iy=12Iz
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B
Ix=Iy=2I2
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C
ID=IX
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D
ID=IZ
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Solution

The correct option is C ID=IX

According to axis theorem,
Ix+Iy=Iz
Also, from symmetry we get Ix=Iy
2Ix=Iz or Ix=Iz2
Again, from perp axis theorem, ID+ID=2ID=Iz
Ix=ID


1102549_1015530_ans_4d6c6f38f0c64497aac42abb3525fd4e.png

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