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The moment of inertia of a thin rod of mass M and length L about an axis passing through the point at a distance L/4 from one of its ends and perpendicular to the rod is _____ 

(A) [(7ML2) / 48] 

(B) [(ML2 / 12] 

(C) [(ML2 / 9] 

(D) [(ML2 / 3]

1 Answer

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Best answer

Correct option: (A) [(7ML2) / 48]

Explanation:

using parallel axis theorem

I = ICM + Mx2            (1)

where x is distance of axis of rotation from the centre of mass of rod.

x = (L/2) – (L/4) = (L/4)

also    ICM = (ML2 / 12)

from (1)

I = (ML2 / 12) + M(L / 4)2 

= (ML2 / 12) + (ML / 16)2 

= [(7ML2) / 48]   

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