The length of an iron bar is 100cm at 20°C. At what temperature will its length increase by 0.01%? [Linear expansivity of iron = 1.2 x 10$^{-5}$°C]

Analyze the question: An iron bar of length 100 cm at 20°C expands by 0.01% of its original length. We need the temperature at which this happens, given α = 1.2 × 10⁻⁵ °C⁻¹.

Concept: Linear expansion is given by

ΔL = L₀ α Δθ, so Δθ = ΔL / (L₀ α)

Solution:

1. Increase in length: 0.01% of 100 cm = (0.01/100) × 100 = 0.01 cm
2. Substitute: Δθ = 0.01 / (100 × 1.2 × 10⁻⁵) Δθ = 0.01 / (1.2 × 10⁻³) Δθ ≈ 8.33°C
3. Final temperature = 20 + 8.33 = 28.33°C ≈ 28.3°C

Tip: For percentage expansion questions, you can skip the length entirely. A fractional increase of 0.01% = 1 × 10⁻⁴, so Δθ = (1 × 10⁻⁴) / α = (1 × 10⁻⁴)/(1.2 × 10⁻⁵) = 8.33°C. Don't forget to add the starting temperature (20°C) because the question asks for the final temperature, not the change in temperature. Options like D (23.0°C) are traps for students who forget to finish the calculation.