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The linear expansion coefficients of steel and a metal X are 12 x 10⁻⁶ and 2 x 10⁻⁶ per deg C respectively. A cube of metal X is measured at 40 deg C with a steel vernier callipers (calibrated at 0 deg C) and reads 100 mm. The true length of the cube's side at 0 deg C is:

1. > 100 mm
2. < 100 mm
3. = 100 mm
4. data is insufficient

Correct answer: > 100 mm

Solution

Because steel expands more than X, the steel scale over-reads less than X shrinks; carrying the numbers through gives a 0 deg C length of about 100.04 mm, which is greater than 100 mm.

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