Two particles of masses m_1 and m_2 are connected to a rigid massless rod of length r to constitute a dumb bell which is free to move in the plane. The moment of inertia of the dumb bell about and axis perpendicular to the plane passing through the centre of mass is

Q: Two particles of masses m_1 and m_2 are connected to a rigid massless rod of length r to constitute a dumb bell which is free to move in the plane. The moment of inertia of the dumb bell about and axis perpendicular to the plane passing through the centre of mass is

(a) $\displaystyle \frac{m_1 m_2}{m_1 + m_2} r^2 $

(b) $\displaystyle ( m_1 + m_2 ) r^2 $

(c) $\displaystyle \frac{m_1 m_2}{m_1 – m_2} r^2 $

(d) $\displaystyle ( m_1 – m_2 ) r^2 $