A metre scale made of steel gives accurate readings at 20^ C . A sensitive experiment demands distance measurements to be accurate up to 0.055 mm in 1 m . Determine the temperature range within which the experiment can be conducted using this metre scale. The coefficient of linear expansion of steel is given as 11 10⁻⁶ ^ C⁻¹ .

Step-by-step solution

The error in the reading of the scale due to a change in temperature is given by the formula for linear expansion: L = L₀ T Given that the maximum allowed error is L = 0.055 mm = 0.055 10⁻³ m , the original length is L₀ = 1 m , and the coefficient of linear expansion is = 11 10⁻⁶ ^ C⁻¹ . Substituting the values into the formula: 0.055 10⁻³ = 1 11 10⁻⁶ T T = 0.055 10⁻³ 11 10⁻⁶ = 55 10⁻⁶ 11 10⁻⁶ = 5^ C The scale gives accurate readings at 20^ C . Therefore, the maximum allowable temperature deviation is 5^ C above or