Question

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

• A. 0.42 m from mass of 0.3 kg
• B. 0.70 m from mass of 0.7 kg
• C. 0.98 m from mass of 0.3 kg
• D. 0.98 m from mass of 0.7 kg

Answer 1

Answer: (C)

0.98 m from mass of 0.3 kg

Answer 2

Work done $W=\frac{1}{2}I\omega^2$
If x is the distance of mass 0.3 kg from the centre of mass, we will have,
$I=(0.3)x^2+(0.7)(1.4-x)^2$
For work to be minimum, the moment of inertia (/) should be minimum, or
or $2(0.3x)-2(0.7)(1.4-x)=0$
or $(0.3)x=(0.7)(1.4-x)$
$\Rightarrow x=\frac{(0.7)(1.4)}{0.3+0.7}=0.98m$