QJEEAdv23Ph0909: JEE Advanced 2023 Physics - Class 11 JEEAdv23Ph0909 Solution: Two point-like objects of masses and are fixed at the two ends…

Two point-like objects of masses $20 ~\mathrm{gm}$ and $30 ~\mathrm{gm}$ are fixed at the two ends of a rigid massless rod of length $10 \mathrm{~cm}$ . 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 $1.2 \times 10^{-8} \mathrm{~N} \mathrm{~m} ~\mathrm{rad}^{-1}$ . The angular frequency of the oscillations in $n \times 10^{-3} ~\mathrm{rad} ~\mathrm{s}^{-1}$ . The value of $n$ is _________ .