A steel metre scale reads correctly at 16 deg C. The linear expansion coefficient of steel is 11 x 10⁻⁶ per deg C. Determine the percentage error in its reading when used (a) on a summer day at 46 deg C and (b) on a winter day at 6 deg C. Which statement is correct?

Percentage error in the reading at 46 deg C is 0.033 %
Percentage error in the reading at 46 deg C is -0.033 %
Percentage error in the reading at 6 deg C is 0.011 %
Percentage error in the reading at 6 deg C is -0.011 %

Correct answer: Percentage error in the reading at 46 deg C is -0.033 %

Solution

At 46 deg C, delta_T = +30, giving |error| = 11e-6 * 30 * 100 = 0.033 %; since an expanded scale reads low, the error is -0.033 %.

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