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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.
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Solution
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
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