Question Detail
Question
Calculate the change in length of the upper leg bone when a 70 kg man supports 62 kg of his mass on it, assuming the bone to be equivalent to a uniform rod that is 40 cm long and 2 cm in radius. Take Young's modulus of the bone as 9 × 10⁹ N/m² and acceleration due to gravity 9.8 m/s².
Correct Answer
Option A is the correct answer.
Detailed Explanation
Young's modulus Y = (F/A)/(ΔL/L) = FL/(AΔL). Rearranging: ΔL = FL/(AY). Force F = mg = 62 kg × 9.8 m/s² = 607.6 N. Length L = 0.40 m. Area A = πr² = π × (0.02 m)² = π × 0.0004 = 0.0012566 m². Y = 9 × 10⁹ N/m². ΔL = (607.6 × 0.40)/(0.0012566 × 9 × 10⁹) = 243.04/(1.13094 × 10⁷) = 2.15 × 10⁻⁵ m = 0.0000215 m ≈ 0.00002 m.
Hint
Use Young's modulus formula: ΔL = FL/(AY). Calculate force from the supported mass.