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A steel metre scale is calibrated to read correctly at 20 degC. If it is used at 10 degC, what is the true distance between its 50 cm and 51 cm marks? Take the linear expansion coefficient of steel as 1.1 x 10⁻⁵ per degC.

1. 0.99989 cm
2. 1.00011 cm
3. 0.89989 cm
4. 1.10011 cm

Correct answer: 0.99989 cm

Solution

Cooling by 10 degC contracts the scale, so the 1 cm interval truly measures 1*(1 + alpha*(-10)) = 0.99989 cm.

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