Rotation 5 Question 8

18. Two point masses of 0.3kg and 0.7kg are fixed at the ends of a rod of length 1.4m and of negligible mass. The rod is set rotating about an axis perpendicular to its length with a uniform angular speed. The point on the rod through which the axis should pass in order that the work required for rotation of the rod is minimum, is located at a distance of

(a) 0.42m from mass of 0.3kg

(1995, S)

(b) 0.70m from mass of 0.7kg

(c) 0.98m from mass of 0.3kg

(d) 0.98m from mass of 0.7kg

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Answer:

Correct Answer: 18. (c)

Solution:

  1. Work done, W=12Iω2

If x is the distance of mass 0.3kg from the centre of mass, we will have,

I=(0.3)x2+(0.7)(1.4x)2

For work to be minimum, the moment of inertia (I) should be minimum, or dIdx=0

 or 2(0.3x)2(0.7)(1.4x) or (0.3)x=(0.7)(1.4x)x=(0.7)(1.4)0.3+0.7=0.98m



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