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 :<br>

Question

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( A ) x = $\frac{m_1}{ m_2}L$
( B ) x = $\frac{ m_2}{m_1}L$
( C ) x = $\frac{m_2L}{m_1 + m_2}$
( D ) x = $\frac{m_1L}{m_1 + m_2}$