Physics · Heat and Thermodynamics
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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)
- 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
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.
This option suggests an increase in length of 537.1×10-5m, which is incorrect. The formula for linear expansion is ΔL=L0⋅α⋅ΔT. Applying the given values correctly will not yield this result.
This option suggests an increase in length of 447.5×10-5m, which is incorrect. The calculation using the formula ΔL=L0⋅α⋅ΔT with the given values will not yield this result.
This option suggests an increase in length of 327.5×10-5m, which is incorrect. Ensure the formula ΔL=L0⋅α⋅ΔT is used correctly with the given values.
This is the correct answer. By using the formula ΔL=L0⋅α⋅ΔT, with L0=15 m, α=1.1 x 10-5 K-1, and ΔT=15°C, we find ΔL=247.5 x 10-5 m.
This option suggests an increase in length of 127.5×10-5m, which is incorrect. The correct calculation using the formula ΔL=L0⋅α⋅ΔT does not result in this value.
Tagged under Physics · Heat and Thermodynamics · 2014