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A steel tape is calibrated at 20degree Celsius. On a cold day when the temperature is -15 degree Celsius, percentage error in the tape will be [alpha= 1.2 x 10^-5 per degree Celsius ] Answer is -0.042%. Can anybody explain this?
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A steel tape is calibrated at 20degree Celsius. On a cold day when the...
Explanation of the Calculation of Percentage Error in Steel Tape
When a steel tape is calibrated at a certain temperature, its length is determined based on the coefficient of thermal expansion of steel, which is dependent on the temperature. Therefore, when the temperature changes, the length of the steel tape also changes, resulting in a percentage error. The percentage error can be calculated using the following formula:
Percentage error = (L2 - L1)/L1 x 100%
where L1 is the length of the steel tape at the calibration temperature and L2 is the length of the steel tape at the operating temperature.
Determination of Alpha
Alpha is the coefficient of thermal expansion of steel, which is a constant value. In this case, alpha is given as 1.2 x 10^-5 per degree Celsius. This means that for every degree Celsius change in temperature, the length of the steel tape changes by 1.2 x 10^-5 times its original length. Therefore, if the temperature changes by ΔT degrees Celsius, the change in length of the steel tape can be calculated using the following formula:
ΔL = LαΔT
where L is the original length of the steel tape.
Calculation of Percentage Error
Using the formula for percentage error and the value of ΔL calculated above, the percentage error in the steel tape can be calculated as follows:
Percentage error = (ΔL/L) x 100%
Substituting the value of ΔL from the formula above, we get:
Percentage error = (LαΔT/L) x 100%
Simplifying the expression, we get:
Percentage error = αΔT x 100%
Substituting the values of alpha and ΔT, we get:
Percentage error = 1.2 x 10^-5 x (-15) x 100%
Simplifying the expression, we get:
Percentage error = -0.042%
Conclusion
Therefore, the percentage error in the steel tape is -0.042% when the temperature is -15 degree Celsius.
Community Answer
A steel tape is calibrated at 20degree Celsius. On a cold day when the...
Change in temperature=20-(-15)=35C
decrease in length=1+a×t×l=(1.2×10^-5×35×l)=0.00042l
percentage error=0.00042l/l×100
=-0.00042×100
=-0.042%...
decrease in length=1+a×t×l=(1.2×10^-5×35×l)=0.00042l
percentage error=0.00042l/l×100
=-0.00042×100
=-0.042%...
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A steel tape is calibrated at 20degree Celsius. On a cold day when the temperature is -15 degree Celsius, percentage error in the tape will be [alpha= 1.2 x 10^-5 per degree Celsius ] Answer is -0.042%. Can anybody explain this?
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A steel tape is calibrated at 20degree Celsius. On a cold day when the temperature is -15 degree Celsius, percentage error in the tape will be [alpha= 1.2 x 10^-5 per degree Celsius ] Answer is -0.042%. Can anybody explain this? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A steel tape is calibrated at 20degree Celsius. On a cold day when the temperature is -15 degree Celsius, percentage error in the tape will be [alpha= 1.2 x 10^-5 per degree Celsius ] Answer is -0.042%. Can anybody explain this? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A steel tape is calibrated at 20degree Celsius. On a cold day when the temperature is -15 degree Celsius, percentage error in the tape will be [alpha= 1.2 x 10^-5 per degree Celsius ] Answer is -0.042%. Can anybody explain this?.
A steel tape is calibrated at 20degree Celsius. On a cold day when the temperature is -15 degree Celsius, percentage error in the tape will be [alpha= 1.2 x 10^-5 per degree Celsius ] Answer is -0.042%. Can anybody explain this? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A steel tape is calibrated at 20degree Celsius. On a cold day when the temperature is -15 degree Celsius, percentage error in the tape will be [alpha= 1.2 x 10^-5 per degree Celsius ] Answer is -0.042%. Can anybody explain this? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A steel tape is calibrated at 20degree Celsius. On a cold day when the temperature is -15 degree Celsius, percentage error in the tape will be [alpha= 1.2 x 10^-5 per degree Celsius ] Answer is -0.042%. Can anybody explain this?.
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