A solid disk of radius R is suspended from a spring of linear spring constant k and torsional constant c. What value of R gives the same period for vertical and torsional oscillations?

Question

G1 Physics · Accepted Answer

Vertical oscillation: Tᵥ=2π√(m/k). Torsional oscillation of the disk: I=(1/2)mR², so Tₜ=2π√(I/c)=2π√(mR²/2c). Equating periods gives 1/k=R²/(2c), hence R=√(2c/k). Correct answer: A.