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What is the percentage increase in length of a wire of diameter 2.5 mm, stretched by a force of 100 kg wt? Young's modulus of wire is 12.5 x 10^11 dyne/cm^2 A) 0.16% B) 0.32% C) 0.08% D) 0.12%?
Most Upvoted Answer
What is the percentage increase in length of a wire of diameter 2.5 mm...
Given Data
- Diameter of wire (d) = 2.5 mm = 0.25 cm
- Radius (r) = d/2 = 0.125 cm
- Force (F) = 100 kg wt = 100 x 980 dyne = 98000 dyne
- Young's modulus (Y) = 12.5 x 10^11 dyne/cm^2
Calculating Cross-Sectional Area
- Area (A) = πr²
- A = π(0.125 cm)² = π(0.015625 cm²) ≈ 0.0491 cm²
Calculating Stress
- Stress (σ) = Force/Area
- σ = 98000 dyne / 0.0491 cm² ≈ 1995696.68 dyne/cm²
Calculating Strain
- Using Young's modulus:
- Y = Stress/Strain
- Strain (ε) = Stress/Y
- ε = 1995696.68 dyne/cm² / (12.5 x 10^11 dyne/cm²) ≈ 0.001596
Calculating Percentage Increase in Length
- Percentage increase = Strain x 100%
- Percentage increase = 0.001596 x 100% = 0.1596%
Final Answer
- The percentage increase in length of the wire is approximately 0.16%. Thus, the correct answer is A) 0.16%.
Community Answer
What is the percentage increase in length of a wire of diameter 2.5 mm...
A
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What is the percentage increase in length of a wire of diameter 2.5 mm, stretched by a force of 100 kg wt? Young's modulus of wire is 12.5 x 10^11 dyne/cm^2 A) 0.16% B) 0.32% C) 0.08% D) 0.12%?
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What is the percentage increase in length of a wire of diameter 2.5 mm, stretched by a force of 100 kg wt? Young's modulus of wire is 12.5 x 10^11 dyne/cm^2 A) 0.16% B) 0.32% C) 0.08% D) 0.12%? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about What is the percentage increase in length of a wire of diameter 2.5 mm, stretched by a force of 100 kg wt? Young's modulus of wire is 12.5 x 10^11 dyne/cm^2 A) 0.16% B) 0.32% C) 0.08% D) 0.12%? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the percentage increase in length of a wire of diameter 2.5 mm, stretched by a force of 100 kg wt? Young's modulus of wire is 12.5 x 10^11 dyne/cm^2 A) 0.16% B) 0.32% C) 0.08% D) 0.12%?.
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