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 \(\omega_0\) is minimum, is given by : 

x = \(\frac{m_2 L}{m_1 + m_2}\)

Minimum work ⇒ Minimum rotational kinetic energy ⇒ Maximum angular momentum ⇒ Minimum moment of inertia

So, its rotation should be about CM 

x = \(\frac{m_2 L}{m_1 + m_2}\)