Question

Two point-like objects of masses 20 gm and 30 gm are fixed at the two ends of a rigid massless rod of length 10 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 × 10⁻⁸ N m rad⁻¹. The angular frequency of the oscillations in n × 10⁻³ rad s⁻¹. The value of n is _____.

Answer 1

m₁ = 30 gm

m₂ = 20 gm

Moment of inertia about the axis of rotation is

I = m₁r₁² + m₂r₂²

Clearly r₁ = 4 cm

And r₂ = 6 cm

\(\therefore\) I = (30 × 10^–3 × 16 × 10^–4) + (20 × 10^–3 × 36 × 10^–4) 

⇒ I = 1200 × 10^–7 kg m²

If the system is rotated by small angle ‘\(\theta\)’, the restoring torque is \(\tau\)_(R) = –k\(\theta\)