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Two point masses of 0.3 kg and 0.7 kg are fixed at the ends of a rod of length 1.4 m 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

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0.42 m from mass of 0.3 kg

0.70 m from mass of 0.7 kg

0.98 m from mass of 0.3 kg

0.98 m from mass of 0.7 kg

answer is C.

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Detailed Solution

Work done is equal to change in kinetic energy = $\frac{1}{2} {Iω}^{2}$ .

This will be minimum when I will be minimum that is when I is about its center of mass,

that is distance of center of mass from 0.3 kg mass is $\frac{0.7}{0.3 + 0.7} 1.4 = 0.7 \times 1.4 = 0.98 m$

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