Question

# I is moment of inertia of a thin rod of mass M, length L about an axis perpendicular to the length of rod and passing through its centre. The moment of inertia of a thin square plate of mass 4M, side length L2 about an axis passing through opposite corners of plate is:

A
4I
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B
2I
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C
I
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D
I2
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Solution

## The correct option is C IFor thin rod of mass M and length L : Moment of inertia about axis perpendicular to the length of rod and passing through its centre is I=ML2/12For thin square plate of mass M′=4M and side length L′=L/2: Moment of Inertia about axis passing through opposite corners I′=M′(L′)212 ∴ I′=(4M)(L/2)212=ML2/12=I

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