Question

length of one metre is measured using a metal tape at 20 degree celsius is calibrated at a temperature 40 degree Celsius the actual length for equal to (2×10-4/°c)​

Answer 1

Given,

Length of one metre is measured using metal tape at 20°C is calibrated at a temperature 40°C. coefficient of thermal expansion is 2 × 10¯⁴/°C

To find,

The actual length.

using formula,

L' = L(1 + α∆T)

here, L' = 1m , α = 2 × 10¯⁴/°C , ∆T = 40°C - 20°C = 20°C

⇒1 = L(1 + 2 × 10¯⁴ × 20)

⇒L = 1/(1 + 0.0040) = 1/1.004 = 0.996 m

therefore actual length is 0.996 m or 99.6 cm.

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