A steel meter scale is correct at 20°C; maximum allowed length change is 0.055 mm per metre. α=11×10⁻⁶ °C⁻¹. Temperature interval is n×3°C to n×5°C. Find n.
Physics · Mixed Chapter
JEE Main Practice

Question

A steel meter scale is correct at 20°C; maximum allowed length change is 0.055 mm per metre. α=11×10⁻⁶ °C⁻¹. Temperature interval is n×3°C to n×5°C. Find n.

G1 Physics · Accepted Answer

Step 1: Allowed error ΔL=0.055 mm=5.5×10⁻⁵ m for L=1 m. Step 2: Thermal expansion ΔL=Lα|ΔT| gives |ΔT|≤(5.5×10⁻⁵)/(11×10⁻⁶)=5°C. Step 3: Calibration 20°C permits 15°C to 25°C. Step 4: 15=n×3 and 25=n×5 both give n=5.