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A steel tape 1m long is correctly calibr...

A steel tape 1m long is correctly calibrated for a temperature of `27.0^(@)C`. The length of a steel rod measured by this tape is found to be 63.0 cm on a hot day when the temperature is `45.0^(@)C`. What is the actual length of the steel rod on that day ? What is the length of the same steel rod on a day when the temperature is `27.0^(@)C` ? Coefficient of linear expansion of steel `= 1.20xx 10^(–5) K^(–1)`.

Text Solution

Verified by Experts

Length of the steel tape at `27^(0)C ` is 100cm.
i.e. L = 100 cm and T = `27^(0)`C.
The length of steel tape at `45^(0)` is
L = L + `Delta L = L + alpha L Delta T `
= `100 + (1.20 xx 10^(-5)) xx 100 xx (45^(0) - 27^(0)) = 100.0216` cm
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