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 ωo it minimum, is given by :

Question

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 ωo it minimum, is given by :

Infinity Learn · Accepted Answer

As moment of inertia is minimum about centre of mass so point P must be centre of mass.⇒$$m1x=m2(L$$−$$x)$$⇒$$x=m2Lm1+m2$$

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