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Question

# Two point masses A of mass M and B of mass 4M are fixed at the ends of a rod of length l and of negligible mass. The rod is set rotating about an axis perpendicular to its length with a uniform angular speed. The work required for rotating the rod will be minimum when the distance of axis of rotation from the mass A is at

A
25l
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B
85l
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C
45l

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D
l5
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Solution

## The correct option is C 45l W=12Iω2 Let x be the distance of CM from A I=Mx2+4M(l−x)2 and if I is minimum, W will be minimum ∴dldx=2Mx+4M×2(l−x)×(−1) =2Mx−8M(l−x) dldx=10Mx−8Ml ∴10Mx−8Ml=0 x=45l

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