### Q.6:- 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}.

**Answer:-**

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

At temperature *T*_{1} = 45°C, the length of the steel rod, *l*_{1} = 63 cm

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

Let *l*_{2} be the actual length of the steel rod and *l*‘ be the length of the steel tape at 45°C.

l’ = l + αl(T_{1} – T)

∴ l’ = 100 + 1.20 × 10^{-5} × 100(45 – 27)

= 100.0216 cm

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

l_{2} = (100.0216 / 100) × 63 = 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.