A torsion pendulum consists of a uniform rod hanging horizontally from thin wire tied to its center. When the wire is twisted through an angle θ, the wire exerts a torque τ = -γθ, where γ = 0.0016 Nm/rad. The rod has a mass of 35 grams and is 10 cm long. What is the period of the torsional oscillations of the pendulum?
A)0.85 s
B)1.4 s
C)0.99 s
D)2.1 s
E)0.023 s

Question

Quizplus · Accepted Answer

The period of a torsional pendulum is given by:T = 2π√(I/γ)where I is the moment of inertia of the rod and γ is the torsional constant of the wire.The moment of inertia of a uniform rod about its center is:I = (1/12)ML^2where M is the mass of the rod and L is its length.Substituting these values into the equation for the period, we get:T = 2π√((1/12)ML^2/γ)= 2π√((1/12)(0.035 kg)(0.1 m)^2/0.0016 Nm/rad)= 0.85 sTherefore, the correct answer is A.

A Torsion Pendulum Consists of a Uniform Rod Hanging Horizontally