Masses 20 g and 30 g are fixed at the ends of a rigid massless rod of length 10 cm. The system is suspended by a torsion wire attached at its centre of mass. Torsional constant is 1.2×10⁻⁸ N m rad⁻¹. If angular frequency is n×10⁻³ rad s⁻¹, find n.

Question

G1 Physics · Accepted Answer

Distances of the 20 g and 30 g masses from the centre of mass are 6 cm and 4 cm, respectively. Thus I=(0.02)(0.06)²+(0.03)(0.04)²=1.2×10⁻⁴ kg m². With torsional constant C=1.2×10⁻⁸ N m rad⁻¹, ω=√(C/I)=√(10⁻⁴)=10⁻² rad s⁻¹=10×10⁻³ rad s⁻¹. Hence n=10.