Two point-like objects of masses \( 20 \, \text{gm} \) and \( 30 \, \text{gm} \) are fixed at the two ends of a rigid massless rod of length \( 10 \, \text{cm} \). This system is suspended vertically from a rigid ceiling using a thin wire attached to its center of mass, as shown in the figure. The resulting torsional pendulum undergoes small oscillations. The torsional constant of the wire is \( 1.2 \times 10^{-8} \, \text{N m rad}^{-1} \). The angular frequency of the oscillations in \( n \times 10^{-3} \, \text{rad s}^{-1} \). The value of \( n \) is _______.
