Ncert Exercises & Solutions

11.6 A steel tape 1 m 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 × $10^{- 5}$ $K^{- 1}$ .

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.

$l' = l [1 + α (T_{1} - T)] ∴ l' = 100 + 1.20 \times 10^{- 5} \times 100 (45 - 27) = 100.0216 cm$

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

$l_{2} = \frac{100.0216}{100} \times 63 = 63.0136 cm$

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.

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