An aluminium and steel rods having same lengths and cross-sections are joined to make total length of 120 cm at 30°C. The coefficient of linear expansion of aluminium and steel are 24 × 10⁻⁶ °C⁻¹ and 1.2 × 10⁻⁵ °C⁻¹, respectively. The length of this composite rod when its temperature is raised to 100°C, i $s _____$ cm.
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Question

An aluminium and steel rods having same lengths and cross-sections are joined to make total length of 120 cm at 30°C. The coefficient of linear expansion of aluminium and steel are 24 × 10⁻⁶ °C⁻¹ and 1.2 × 10⁻⁵ °C⁻¹, respectively. The length of this composite rod when its temperature is raised to 100°C, i $s _____$ cm.

Options

G1 Physics · Accepted Answer

The two rods have equal lengths and together make 120 cm. Therefore each rod initially has length 60 cm. The temperature rise is ΔT = 100-30 = 70°C. For aluminium, ΔL₍ᴀ₎ = Lα(A)ΔT = 60 × 24 × 10⁻⁶ × 70 = 0.1008 cm. For steel, α(S) = 1.2 × 10⁻⁵ °C⁻¹ = 12 × 10⁻⁶ °C⁻¹. Thus, ΔL₍S₎ = 60 × 12 × 10⁻⁶ × 70 = 0.0504 cm. Total final length is L₍final₎ = 120+0.1008+0.0504 = 120.1512 cm ≈ 120.15 cm. Correct option: B.