A composite rod is formed by joining a steel rod and a brass rod end-to-end. The total length of the composite rod is 100 cm . The effective coefficient of linear expansion of the composite rod is 1.4 10⁻⁵ K ⁻¹ . If the coefficients of linear expansion of steel and brass are 1.2 10⁻⁵ K ⁻¹ and 2.0 10⁻⁵ K ⁻¹ respectively, what is the length of the steel portion of the rod?

Step-by-step solution

Let the length of the steel rod be L_s and the length of the brass rod be L_b . The total length of the composite rod is L = L_s + L_b = 100 cm . The total increase in length of the composite rod is the sum of the increases in length of the individual rods: L = L_s + L_b L _ eff T = L_s _s T + L_b _b T Substituting the given values: 100 1.4 10⁻⁵ = L_s 1.2 10⁻⁵ + (100 - L_s) 2.0 10⁻⁵ Cancelling 10⁻⁵ from both sides: 140 = 1.2 L_s + 200 - 2.0 L_s 0.8 L_s = 60 L_s = 60 0.8 = 75 cm Answer: 75 cm