Question Detail
Question
The steel bed of a suspension bridge is 300 m long at 20°C. If the temperature on a hot day reaches a maximum value of 45°C, compute the increase in length of the bridge. Take the coefficient of expansion (α) to be 12 × 10⁻⁶ °C⁻¹.
Correct Answer
Option B is the correct answer.
Detailed Explanation
The increase in length due to thermal expansion is given by ΔL = αL₀ΔT. Here, α = 12 × 10⁻⁶ °C⁻¹, L₀ = 300 m, ΔT = 45°C - 20°C = 25°C. ΔL = (12 × 10⁻⁶) × 300 × 25 = 12 × 10⁻⁶ × 7500 = 90,000 × 10⁻⁶ = 0.09 m = 9 cm.
Hint
Use the linear expansion formula: ΔL = αL₀ΔT. Ensure consistent units.