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A line was measured with a steel rape which was exactly 30 m at 18̊C and a pull of 50 N and the measured length was 459.242 m. Temperature during measurement was 28̊C and the pull applied was 100 N. The tape was uniformly supported during the measurement. Find the true length of the line if the cross-sectional area of the tape was 0.02 cm2, the coefficient of expansion per ̊C = 0.0000117 and the modulus of elasticity = 21 x 10⁶ N per cm².?
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A line was measured with a steel rape which was exactly 30 m at 18̊C a...
Given data:
- Length of the tape at 18̊C and a pull of 50N = 30m
- Measured length of the line at 28̊C and a pull of 100N = 459.242m
- Cross-sectional area of the tape = 0.02 cm²
- Coefficient of expansion per ̊C = 0.0000117
- Modulus of elasticity = 21 x 10⁶ N per cm²
Calculating the thermal expansion:
- The change in temperature = 28̊C - 18̊C = 10̊C
- The coefficient of expansion for the given change in temperature = 0.0000117 per ̊C
- The thermal expansion of the tape = (Change in temperature) * (Coefficient of expansion) * (Original length)
- The thermal expansion of the tape = 10̊C * 0.0000117 * 30m = 0.00351m
Calculating the elastic elongation:
- The pull applied during the measurement = 100N
- The original length of the tape = 30m
- The modulus of elasticity = 21 x 10⁶ N per cm² = 210 x 10⁴ N per m²
- The elastic elongation of the tape = (Pull applied) * (Original length) / (Modulus of elasticity * Cross-sectional area)
- The elastic elongation of the tape = 100N * 30m / (210 x 10⁴ N per m² * 0.02 cm²) = 0.7142857m
Calculating the true length of the line:
- The measured length of the line = 459.242m
- The true length of the line = Measured length - (Thermal expansion + Elastic elongation)
- The true length of the line = 459.242m - (0.00351m + 0.7142857m) = 458.5242043m
Therefore, the true length of the line is approximately 458.524m.
- Length of the tape at 18̊C and a pull of 50N = 30m
- Measured length of the line at 28̊C and a pull of 100N = 459.242m
- Cross-sectional area of the tape = 0.02 cm²
- Coefficient of expansion per ̊C = 0.0000117
- Modulus of elasticity = 21 x 10⁶ N per cm²
Calculating the thermal expansion:
- The change in temperature = 28̊C - 18̊C = 10̊C
- The coefficient of expansion for the given change in temperature = 0.0000117 per ̊C
- The thermal expansion of the tape = (Change in temperature) * (Coefficient of expansion) * (Original length)
- The thermal expansion of the tape = 10̊C * 0.0000117 * 30m = 0.00351m
Calculating the elastic elongation:
- The pull applied during the measurement = 100N
- The original length of the tape = 30m
- The modulus of elasticity = 21 x 10⁶ N per cm² = 210 x 10⁴ N per m²
- The elastic elongation of the tape = (Pull applied) * (Original length) / (Modulus of elasticity * Cross-sectional area)
- The elastic elongation of the tape = 100N * 30m / (210 x 10⁴ N per m² * 0.02 cm²) = 0.7142857m
Calculating the true length of the line:
- The measured length of the line = 459.242m
- The true length of the line = Measured length - (Thermal expansion + Elastic elongation)
- The true length of the line = 459.242m - (0.00351m + 0.7142857m) = 458.5242043m
Therefore, the true length of the line is approximately 458.524m.
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A line was measured with a steel rape which was exactly 30 m at 18̊C and a pull of 50 N and the measured length was 459.242 m. Temperature during measurement was 28̊C and the pull applied was 100 N. The tape was uniformly supported during the measurement. Find the true length of the line if the cross-sectional area of the tape was 0.02 cm2, the coefficient of expansion per ̊C = 0.0000117 and the modulus of elasticity = 21 x 10⁶ N per cm².?
Question Description
A line was measured with a steel rape which was exactly 30 m at 18̊C and a pull of 50 N and the measured length was 459.242 m. Temperature during measurement was 28̊C and the pull applied was 100 N. The tape was uniformly supported during the measurement. Find the true length of the line if the cross-sectional area of the tape was 0.02 cm2, the coefficient of expansion per ̊C = 0.0000117 and the modulus of elasticity = 21 x 10⁶ N per cm².? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A line was measured with a steel rape which was exactly 30 m at 18̊C and a pull of 50 N and the measured length was 459.242 m. Temperature during measurement was 28̊C and the pull applied was 100 N. The tape was uniformly supported during the measurement. Find the true length of the line if the cross-sectional area of the tape was 0.02 cm2, the coefficient of expansion per ̊C = 0.0000117 and the modulus of elasticity = 21 x 10⁶ N per cm².? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A line was measured with a steel rape which was exactly 30 m at 18̊C and a pull of 50 N and the measured length was 459.242 m. Temperature during measurement was 28̊C and the pull applied was 100 N. The tape was uniformly supported during the measurement. Find the true length of the line if the cross-sectional area of the tape was 0.02 cm2, the coefficient of expansion per ̊C = 0.0000117 and the modulus of elasticity = 21 x 10⁶ N per cm².?.
A line was measured with a steel rape which was exactly 30 m at 18̊C and a pull of 50 N and the measured length was 459.242 m. Temperature during measurement was 28̊C and the pull applied was 100 N. The tape was uniformly supported during the measurement. Find the true length of the line if the cross-sectional area of the tape was 0.02 cm2, the coefficient of expansion per ̊C = 0.0000117 and the modulus of elasticity = 21 x 10⁶ N per cm².? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A line was measured with a steel rape which was exactly 30 m at 18̊C and a pull of 50 N and the measured length was 459.242 m. Temperature during measurement was 28̊C and the pull applied was 100 N. The tape was uniformly supported during the measurement. Find the true length of the line if the cross-sectional area of the tape was 0.02 cm2, the coefficient of expansion per ̊C = 0.0000117 and the modulus of elasticity = 21 x 10⁶ N per cm².? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A line was measured with a steel rape which was exactly 30 m at 18̊C and a pull of 50 N and the measured length was 459.242 m. Temperature during measurement was 28̊C and the pull applied was 100 N. The tape was uniformly supported during the measurement. Find the true length of the line if the cross-sectional area of the tape was 0.02 cm2, the coefficient of expansion per ̊C = 0.0000117 and the modulus of elasticity = 21 x 10⁶ N per cm².?.
Solutions for A line was measured with a steel rape which was exactly 30 m at 18̊C and a pull of 50 N and the measured length was 459.242 m. Temperature during measurement was 28̊C and the pull applied was 100 N. The tape was uniformly supported during the measurement. Find the true length of the line if the cross-sectional area of the tape was 0.02 cm2, the coefficient of expansion per ̊C = 0.0000117 and the modulus of elasticity = 21 x 10⁶ N per cm².? in English & in Hindi are available as part of our courses for GATE.
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Here you can find the meaning of A line was measured with a steel rape which was exactly 30 m at 18̊C and a pull of 50 N and the measured length was 459.242 m. Temperature during measurement was 28̊C and the pull applied was 100 N. The tape was uniformly supported during the measurement. Find the true length of the line if the cross-sectional area of the tape was 0.02 cm2, the coefficient of expansion per ̊C = 0.0000117 and the modulus of elasticity = 21 x 10⁶ N per cm².? defined & explained in the simplest way possible. Besides giving the explanation of
A line was measured with a steel rape which was exactly 30 m at 18̊C and a pull of 50 N and the measured length was 459.242 m. Temperature during measurement was 28̊C and the pull applied was 100 N. The tape was uniformly supported during the measurement. Find the true length of the line if the cross-sectional area of the tape was 0.02 cm2, the coefficient of expansion per ̊C = 0.0000117 and the modulus of elasticity = 21 x 10⁶ N per cm².?, a detailed solution for A line was measured with a steel rape which was exactly 30 m at 18̊C and a pull of 50 N and the measured length was 459.242 m. Temperature during measurement was 28̊C and the pull applied was 100 N. The tape was uniformly supported during the measurement. Find the true length of the line if the cross-sectional area of the tape was 0.02 cm2, the coefficient of expansion per ̊C = 0.0000117 and the modulus of elasticity = 21 x 10⁶ N per cm².? has been provided alongside types of A line was measured with a steel rape which was exactly 30 m at 18̊C and a pull of 50 N and the measured length was 459.242 m. Temperature during measurement was 28̊C and the pull applied was 100 N. The tape was uniformly supported during the measurement. Find the true length of the line if the cross-sectional area of the tape was 0.02 cm2, the coefficient of expansion per ̊C = 0.0000117 and the modulus of elasticity = 21 x 10⁶ N per cm².? theory, EduRev gives you an
ample number of questions to practice A line was measured with a steel rape which was exactly 30 m at 18̊C and a pull of 50 N and the measured length was 459.242 m. Temperature during measurement was 28̊C and the pull applied was 100 N. The tape was uniformly supported during the measurement. Find the true length of the line if the cross-sectional area of the tape was 0.02 cm2, the coefficient of expansion per ̊C = 0.0000117 and the modulus of elasticity = 21 x 10⁶ N per cm².? tests, examples and also practice GATE tests.
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