Point masses ${\mathrm{m}}_1$ and ${\mathrm{m}}_2$ are placed at the opposite ends of rigid rod of length $\text{L}$, and negligible mass. The rod is to be set rotating about an axis perpendicular to it. The position of point $\text{L}$ on this rod through which the axis should pass so that the work required to set the rod rotating with angular velocity ${\mathrm{\omega }}_0$ is minimum, is given by:

• A

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

  $\mathrm{x}=\frac{{\mathrm{m}}_2}{{\mathrm{m}}_1}\mathrm{L}$
• Correct answer
  C

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

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

Hence, the correct answer is option: 'C'.