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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

 
  1. 25l
  2. 85l
  3. 45l
  4. 15l


Solution

The correct option is C 45l
W=12Iω2
Let x is the distance of CM from A
I=Mx2+4M(lx)2
And if I is minimum, W will be minimum
dldx=2Mx+4M×2(lx)×(1)=2Mx8M(lx)
dldx=10Mx8Ml=0
10Mx8Ml=0
x=45l

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