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Point masses m₁ and m₂ are placed at the opposite ends of a rigid rod of length L, and negligible mass. The rod is to be set rotating about an axis perpendicular to it. The position of point P on this rod through which the axis should pass so that the work required to set the rod rotating with angular velocity ω₀ is minimum, is given by:

1. x = m₁L/m₂
2. x = m₂L/m₁
3. x = m₂L/(m₁ + m₂)
4. x = m₁L/(m₁ + m₂)

Correct answer: x = m₁L/(m₁ + m₂)

Solution

The work required to set the rod rotating is minimized when the axis of rotation passes through the center of mass of the system. The center of mass for the two masses is located at x = (m₁L) / (m₁ + m₂).

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