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Two particles of masses \( m_{1} \) and \( m_{2} \) are connected by a rigid massless rod of length \( r \) to constitute a
\( \mathrm{P} \) dumb-bell which is free to move in the plane. The moment of inertia of the dumb-bell about an axis perpendicular to the plane passing through the centre of mass is:
(1) \( \frac{m_{1} m_{2} r^{2}}{\left(m_{1}+m_{2}\right)} \)
(2) \( \left(m_{1}+m_{2}\right) r^{2} \)
(3) \( \frac{m_{1} m_{2} r^{2}}{\left(m_{1}-m_{2}\right)} \)
(4) \( \left(m_{1}-m_{2}\right) r^{2} \)
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