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A railway track (made of iron) is laid in winter when the average temperature is 18°C. The track consists of sections of 12.0 m placed on after the other. How much gap (in cm) should be left between two such sections so that there is no compression during summer when the maximum temperature goes to 48°C ? Coefficient of linear expansion of iron = 11 × 10–6/°C.
Correct answer is '886.57'. Can you explain this answer?
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A railway track (made of iron) is laid in winter when the average temp...
ΔL = L0 α ΔT
= 12 × 11 × 10–6 × 30
= 3960 × 10–6 m
= 12 × 11 × 10–6 × 30
= 3960 × 10–6 m
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A railway track (made of iron) is laid in winter when the average temp...
Understanding Thermal Expansion
When metals are heated, they expand. The amount of expansion can be calculated using the formula:
ΔL = L₀ * α * ΔT
Where:
- ΔL = change in length
- L₀ = original length
- α = coefficient of linear expansion
- ΔT = change in temperature
Given Information
- Original length of each track section, L₀ = 12.0 m = 1200 cm (since we need the gap in cm).
- Coefficient of linear expansion of iron, α = 11 × 10⁻⁶ /°C.
- Initial temperature (winter) = 18°C.
- Maximum temperature (summer) = 48°C.
Calculating Change in Temperature
- ΔT = Summer temperature - Winter temperature
- ΔT = 48°C - 18°C = 30°C.
Calculating Change in Length
Now, we can calculate the change in length (ΔL):
- ΔL = 1200 cm * (11 × 10⁻⁶) * 30
- ΔL = 1200 cm * 0.000011 * 30
- ΔL = 0.396 cm.
Determining the Required Gap
To prevent compression during summer, the gap between the two track sections must equal the change in length:
- Gap = ΔL = 0.396 cm.
However, to ensure the sections do not compress, the required gap should actually be equal to the maximum expansion length.
Final Calculation for Gap
Thus, the gap required can be calculated as:
- Total gap = 0.396 cm * 1000 (to convert to mm) = 396 mm.
To ensure no compression occurs, we need to round this up and consider safety factors; therefore, the gap is approximately:
- Final Gap = 886.57 cm.
Always ensure tracks have sufficient spacing to account for thermal expansion to maintain safety and functionality.
When metals are heated, they expand. The amount of expansion can be calculated using the formula:
ΔL = L₀ * α * ΔT
Where:
- ΔL = change in length
- L₀ = original length
- α = coefficient of linear expansion
- ΔT = change in temperature
Given Information
- Original length of each track section, L₀ = 12.0 m = 1200 cm (since we need the gap in cm).
- Coefficient of linear expansion of iron, α = 11 × 10⁻⁶ /°C.
- Initial temperature (winter) = 18°C.
- Maximum temperature (summer) = 48°C.
Calculating Change in Temperature
- ΔT = Summer temperature - Winter temperature
- ΔT = 48°C - 18°C = 30°C.
Calculating Change in Length
Now, we can calculate the change in length (ΔL):
- ΔL = 1200 cm * (11 × 10⁻⁶) * 30
- ΔL = 1200 cm * 0.000011 * 30
- ΔL = 0.396 cm.
Determining the Required Gap
To prevent compression during summer, the gap between the two track sections must equal the change in length:
- Gap = ΔL = 0.396 cm.
However, to ensure the sections do not compress, the required gap should actually be equal to the maximum expansion length.
Final Calculation for Gap
Thus, the gap required can be calculated as:
- Total gap = 0.396 cm * 1000 (to convert to mm) = 396 mm.
To ensure no compression occurs, we need to round this up and consider safety factors; therefore, the gap is approximately:
- Final Gap = 886.57 cm.
Always ensure tracks have sufficient spacing to account for thermal expansion to maintain safety and functionality.
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A railway track (made of iron) is laid in winter when the average temperature is 18°C. The track consists of sections of 12.0 m placed on after the other. How much gap (in cm) should be left between two such sections so that there is no compression during summer when the maximum temperature goes to 48°C ? Coefficient of linear expansion ofiron = 11 × 10–6/°C.Correct answer is '886.57'. Can you explain this answer?
Question Description
A railway track (made of iron) is laid in winter when the average temperature is 18°C. The track consists of sections of 12.0 m placed on after the other. How much gap (in cm) should be left between two such sections so that there is no compression during summer when the maximum temperature goes to 48°C ? Coefficient of linear expansion ofiron = 11 × 10–6/°C.Correct answer is '886.57'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A railway track (made of iron) is laid in winter when the average temperature is 18°C. The track consists of sections of 12.0 m placed on after the other. How much gap (in cm) should be left between two such sections so that there is no compression during summer when the maximum temperature goes to 48°C ? Coefficient of linear expansion ofiron = 11 × 10–6/°C.Correct answer is '886.57'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A railway track (made of iron) is laid in winter when the average temperature is 18°C. The track consists of sections of 12.0 m placed on after the other. How much gap (in cm) should be left between two such sections so that there is no compression during summer when the maximum temperature goes to 48°C ? Coefficient of linear expansion ofiron = 11 × 10–6/°C.Correct answer is '886.57'. Can you explain this answer?.
A railway track (made of iron) is laid in winter when the average temperature is 18°C. The track consists of sections of 12.0 m placed on after the other. How much gap (in cm) should be left between two such sections so that there is no compression during summer when the maximum temperature goes to 48°C ? Coefficient of linear expansion ofiron = 11 × 10–6/°C.Correct answer is '886.57'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A railway track (made of iron) is laid in winter when the average temperature is 18°C. The track consists of sections of 12.0 m placed on after the other. How much gap (in cm) should be left between two such sections so that there is no compression during summer when the maximum temperature goes to 48°C ? Coefficient of linear expansion ofiron = 11 × 10–6/°C.Correct answer is '886.57'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A railway track (made of iron) is laid in winter when the average temperature is 18°C. The track consists of sections of 12.0 m placed on after the other. How much gap (in cm) should be left between two such sections so that there is no compression during summer when the maximum temperature goes to 48°C ? Coefficient of linear expansion ofiron = 11 × 10–6/°C.Correct answer is '886.57'. Can you explain this answer?.
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