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Standard XII

Physics

Thermal Expansion

A steel tape ...

Question

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 = 1.20 × 10^–5 K^–1.

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Solution

Length of the steel tape at temperature T = 27°C, l = 1 m = 100 cm

At temperature T₁ = 45°C, the length of the steel rod, l₁ = 63 cm

Coefficient of linear expansion of steel, α = 1.20 × 10^–5 K^–1

Let l₂ be the actual length of the steel rod and l' be the length of the steel tape at 45°C.

Hence, the actual length of the steel rod measured by the steel tape at 45°C can be calculated as:

= 63.0136 cm

Therefore, the actual length of the rod at 45.0°C is 63.0136 cm. Its length at 27.0°C is 63.0 cm.

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