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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
 



Your Answer
A

l5

Correct Answer
B

45l

Your Answer
C

35l

Your Answer
D

25l


Solution

The correct option is B

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

dIdx=2Mx+4M×2(lx)×(1)

=2Mx8M(lx)

dIdx=10Mx8Ml

10Mx8Ml=0

x=45l
Which is the position of center mass of this system.

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