A uniform elastic rod of density 8000 kg/m³, natural length 1 m and Young's modulus 2 × 10¹¹ Pa rotates in a horizontal plane about one end with angular speed 150 rad/s. If its elongation is N/10 mm, find N.

Question

G1 Physics · Accepted Answer

For a uniform rod rotating about one end, ΔL = [ρω²L³] / [3Y]. Substitute: ρ = 8000 kg/m³, ω = 150 rad/s, L = 1 m, Y = 2×10¹¹ Pa. Therefore, ΔL = [8000×150²] / [3×2×10¹¹]. Thus, ΔL = 3×10⁻⁴ m = 0.3 mm. The question gives ΔL = N/10 mm. Hence, N/10 = 0.3. Therefore, N = 3.