The length of steel rod is 5 cm longer than the copper rod at all temperatures. The length of the steel and copper rod is respectively (Coefficient of linear expansion for steel and copper is respectively 1.1 10⁻⁵ / ^ C and 1.7 10⁻⁵ / ^ C )

Step-by-step solution

The constant length difference condition L_s(T) - L_c(T) = 5 cm must hold for all temperatures. Applying thermal expansion formulas L(T) = L₀(1 + T) yields: (L_s - L_c) + (L_s _s - L_c _c) T = 5 For temperature independence, both L_s - L_c = 5 and L_s _s = L_c _c must be satisfied. Substituting L_s = L_c + 5 into the second equation: (L_c + 5) _s = L_c _c L_c = 5 _s _c - _s = 5 1.1 10⁻⁵ (1.7 - 1.1) 10⁻⁵ = 5.5 0.6 9.17 cm Thus L_s = L_c + 5 14.17 cm . These values correspond to nearly 14 cm and 9 cm , matching optio