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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 28̊ C 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:
- Measured length at 18̊C and 50 N pull: 30 m
- Measured length at 28̊C and 100 N pull: 459.242 m
- Coefficient of expansion per ̊C: 0.0000117
- Modulus of elasticity: 21 x 10⁶ N per cm²
- Cross-sectional area of the tape: 0.02 cm²

Calculating the true length:

1. Calculating the change in length:
- Change in temperature: 28̊C - 18̊C = 10̊C
- Change in pull: 100 N - 50 N = 50 N

2. Calculating the strain:
- Strain = Change in length / Original length
- Strain = (459.242 m - 30 m) / 30 m = 429.242 m / 30 m = 14.30807

3. Calculating the stress:
- Stress = Modulus of elasticity x Strain
- Stress = 21 x 10⁶ N/cm² x 14.30807 = 300637.47 N/cm²

4. Calculating the change in length due to stress:
- Change in length = Stress x Length x Coefficient of expansion x Change in temperature
- Change in length = 300637.47 N/cm² x 30 m x 0.02 cm² x 0.0000117 x 10 = 0.211 m

5. Calculating the true length:
- True length = Measured length at 28̊C and 100 N pull - Change in length due to stress
- True length = 459.242 m - 0.211 m = 459.031 m

Therefore, the true length of the line is 459.031 m.
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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 28̊ C 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 and a pull of 50 N and the measured length was 459.242 m. Temperature during measurement was 28̊ C 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 28̊ C 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 28̊ C 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 28̊ C 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. Download more important topics, notes, lectures and mock test series for GATE Exam by signing up for free.
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 28̊ C 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 28̊ C 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 28̊ C 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 28̊ C 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 28̊ C 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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