Point masses $m_1$ and $m_2$ 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 $\omega_0$ is minimum,is given by

• A
  $x = \frac{m_2 L}{m_1 + m_2}$
• B
  $x = \frac{m_1 L}{m_1 + m_2}$
• C
  $x = \frac{m_1 L}{m_2}$
• D
  $x = \frac{m_2 L}{m_1}$