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The moment of inertia of a uniform thin ...

The moment of inertia of a uniform thin rod of length `L` and mass `M` about an axis passing through a point at a distance of `L//3` from one of its ends and perpendicular to the rod is

A

`(ML^(2))/(9)`

B

`(ML^(2))/(12)`

C

`(ML^(2))/(3)`

D

`(ML^(2))/(5)`

Text Solution

Verified by Experts

The correct Answer is:
A
The point is at a distance of `(L)/(2)-(L)/(3)=(L)/(6)` from the centre of the rod.
`therefore` By using the principle of parallel axes, we get
`I=(ML^(2))/(12)+M[(L)/(6)]^(2)=(ML^(2))/(12)+(ML^(2))/(36)=(ML^(2))/(9)`
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