A steel rod has a length of 15 m at a temperature of 30°C. If the temperature is raised to 45°C. The increase in its length is:(α= 1.1 x 10^-5 K-1)
Correct answer: D. 247.5 x 10^-5 m
- A. 537.1 x 10^-5 m
- B. 447.5 x 10^-5 m
- C. 327.5 x 10^-5 m
- D. 247.5 x 10^-5 m
- E. 127.5 x 10^-5 m
Explanation
The increase in length of the steel rod is calculated using the linear expansion formula: ΔL=L0⋅α⋅ΔT, where L0 is the initial length, α is the coefficient of linear expansion, and ΔT is the change in temperature. Here, L0=15 m, α=1.1 x 10-5 K-1, and ΔT=15°C (since 45°C - 30°C = 15°C). Applying these values gives: ΔL = 15 × 1.1 x 10-5 × 15 = 247.5 x 10-5 m. This is the correct result, which matches option D.The other options are incorrect due to either a miscalculation or misunderstanding of the application of the formula.
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