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 ${\mathrm{\omega }}_{\mathrm{o}}$ it minimum, is given by :

• A

  $\mathrm{x}=\frac{{\mathrm{m}}_2\mathrm{L}}{{\mathrm{m}}_1+{\mathrm{m}}_2}$

• B

  $\mathrm{x}=\frac{{\mathrm{m}}_1\mathrm{L}}{{\mathrm{m}}_1+{\mathrm{m}}_2}$

• C

  $\mathrm{x}=\frac{{\mathrm{m}}_1}{{\mathrm{m}}_2}\mathrm{L}$

• D

  $\mathrm{x}=\frac{{\mathrm{m}}_2}{{\mathrm{m}}_1}\mathrm{L}$