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Moment of Inertia of a Rod

The density o...

Question

The density of rod $A B$ increases linearly from $A$ to $B$ . Its midpoint is $O$ and its centre of mass is at $C$ . Four axes pass through $A, B, O$ and $C$ , all perpendicular to the length of the rod. The moments of inertia of the rod about these axes are $I_{A}$ , $I_{B}$ , $I_{C}$ respectively.

A

I_{A} > I_{B}

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B

I_{A} < I_{B}

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C

I_{B} > I_{C}

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D

I_{O} < I_{C}

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Solution

The correct option is A $I_{A} > I_{B}$
$I_{C}$ is least and $C$ lies between $O$ and $B$ as density is increasing from $A$ to $B$
$I_{A} > I_{B}$ more mass is concentrate towards $B$ .

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