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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

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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

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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