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

When a rod having point masses affixed to both ends rotates, the work which must be performed to set its rotation going, and also sustain it, will depend on how the mass distribution is relative to the axis of rotation. So, in order to minimize such work, it should pass through the center of mass of the system.

Here the rod is of length 1.4 m. The point masses are 0.3 kg and 0.7 kg located at the opposite ends of this rod. It is found that the center of mass is placed at a distance of about 0.98 m from the 0.3 kg mass. So to minimize the work done in the rotation, this axis of rotation should pass through this point.

Positioning the axis at the center of mass minimizes the rotational inertia of the system, making the rotation more efficient. This is one of the approaches in physics to make calculations easier and reduce the energy required to start rotational motion.

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