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Q.

The linear mass density of a thin rod AB of length L varies from A to B as  λ(x) =λ01+xL,  where  x is the distance from A.  If M is the mass of the rod then its moment of inertia about an axis passing through A and perpendicular to the rod is:

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a

37 ML2

b

718 ML2

c

512 ML2

d

25 ML2

answer is B.

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Detailed Solution

M=∫oLλo1+xLdx=32λoL I=∫dmx2M=   ∫oLλo1+xLx2dx32λoL  =718ML2
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