Question

A metre scale made of steel reads accurately at 20°C. In a sensitive experiment, distances accurate up to 0.055 mm in 1 m are required. Find the range of temperature in which the experiment can be performed with this metre scale. Coefficient of linear expansion of steel  = 11 × 10^–6 °C^–1.

Answer 1

Given:
Temperature at which a metre scale gives an accurate reading, T₁ = 20 °C
The value of variation admissible, ΔL = 0.055 mm = 0.055 × 10^–3 m, in the length, L₀ = 1 m
Coefficient of linear expansion of steel, α  = 11 × 10^–6  °C^–1
Let the range of temperature in which the experiment can be performed be T₂.
We know:  ΔL = L₀ αΔT

\[\Rightarrow 0 . 055 \times {10}^{- 3} = 1 \times 11 \times {10}^{- 6} \times \left( T_1 \pm T_2 \right)\]

\[ \Rightarrow 5 \times {10}^{- 3} = \left( 20 \pm T_2 \right) \times {10}^{- 3} \]

\[ \Rightarrow 20 \pm T_2 = 5\]

 Either T₂ = 20 + 5 = 25°C

 or T₂= 20 - 5 = 15°C

Hence, the experiment can be performed in the temperature range of 15 °C