Two-point masses of 0.3kg and 0.7kg are fixed at the ends of a rod which is 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

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We have a rod of length 1.4 meters with two point masses: 0.3 kilograms at one end and 0.7 kilograms at the other end. The rod itself has negligible mass. We need to determine where to place the rotation axis perpendicular to the rod's length so that the work required for rotation is minimized. Since work is related to rotational kinetic energy, this means finding the position that minimizes the moment of inertia. The work required for rotation is directly related to rotational kinetic energy, which equals one-half I omega squared, where I is the moment of inertia. For point masses, the moment of inertia is the sum of each mass times its distance squared from the rotation axis. As we can see in the diagram, the position of the rotation axis determines the distances r1 and r2 of each mass from the axis, which directly affects the total moment of inertia.