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Question
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 ______
Options
`(7"ML"^2)/48`
`("ML"^2)/10`
`("ML"^2)/9`
`("ML"^2)/3`
Solution
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 `underline(("ML"^2)/9)`.
Explanation:
The moment of inertia of a thin rod about the axis passing through the centre is `("ML"^2)/12`
Distance of the point from the centre of the rod `("L"/2 - "L"/3)`
Applying parallel axis theorem
I = `("ML"^2)/12 + "M"("L"/2 - "L"/3)^2 = "ML"^2/12 + "ML"^2/36`
= `(3"ML"^2 + "ML"^2)/36 = (4"ML"^2)/36 = "ML"^2/9`
