Question

The design of some physical apparatus requires that there be a constant difference in length at any temperature between iron and copper cylinder laid side by side. What should be the length of cylinders at 0⁰C for difference in length to be 10 cm at all temperatures (Given: Iron a = 1.1 × 10^–5 ºC^–1, Copper a = 1.7 × 10^–5 ºC^–1) –

• A. L_Iron = 18.33 cm, L_Copper = 28.33 cm
• B. L_Iron = 15 cm, L_Coper = 25 cm
• C. L_Iron = 28.33 cm, L_Copper = 18.33 cm
• D. L_Iron = 25 cm, L_Copper = 15 cm

Answer 1

Answer: (C)

L_Iron = 28.33 cm, L_Copper = 18.33 cm

Answer 2

For Iron

L_t – L₀ = L₀ × a × Dt

L_t – L₀ = (L₀)_Iron × 1.1 × 10^–5 Dt

For Copper

L_t – L₀ = (L₀)_Copper × 1.7 × 10^–5 Dt

Since L_t – L₀ is equal for both metals at all temperatures.

(L₀)_Iron × 1.1 × 10^–5 Dt = (L₀)_Copper × 1.7 × 10^–5 Dt

(L₀)_Iron × 11 = (L₀)_Copper × 17

But (L₀)_Iron – (L₀)_Copper = 10 cm

or (L₀)_Iron = (L₀)_Copper + 10 cm

((L₀)_Copper + 10) × 11 = (L₀)_Copper × 17

or 6(L₀)_copper = 110 cm

or (L₀)_copper = 110/6 cm = 18.33 cm.

(L₀)_copper = 18.33 cm.

(L₀)_Iron = 28.33 cm.