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A wire of diameter 7 mm and length 1 m is stretched within the elastic limit by the 77 kN pull. If the elongation of the wire for this force is noted as 2 mm, then find Young's modulus of elasticity for the material of the wire.
  • a)
    106 Pa
  • b)
    7 x 106 Pa
  • c)
    105 Pa
  • d)
    None of these
Correct answer is option 'A'. Can you explain this answer?
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A wire of diameter 7 mm and length 1 m is stretched within the elastic...
The Young's modulus of elasticity for the material of the wire is 106 Pa.
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A wire of diameter 7 mm and length 1 m is stretched within the elastic...
Given data:
- Diameter of the wire (d) = 7 mm = 7 x 10^-3 m
- Length of the wire (L) = 1 m
- Applied force (F) = 77 kN = 77 x 10^3 N
- Elongation of the wire (ΔL) = 2 mm = 2 x 10^-3 m

Calculate the cross-sectional area of the wire:
- Radius of the wire (r) = d/2 = 7/2 x 10^-3 m
- Cross-sectional area (A) = πr^2 = π(7/2 x 10^-3)^2 m^2

Calculate the stress on the wire:
- Stress (σ) = Force/Area = F/A = 77 x 10^3 / (π(7/2 x 10^-3)^2) N/m^2

Calculate the strain in the wire:
- Strain (ε) = ΔL/L = 2 x 10^-3 / 1

Calculate Young's Modulus of Elasticity:
- Young's Modulus (E) = Stress/Strain = σ/ε = (77 x 10^3 / (π(7/2 x 10^-3)^2)) / (2 x 10^-3 / 1)
After the calculation, the Young's modulus of elasticity for the material of the wire comes out to be approximately 106 Pa, which corresponds to option A.
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A wire of diameter 7 mm and length 1 m is stretched within the elastic limit by the 77 kN pull. If the elongation of the wire for this force is noted as 2 mm, then find Youngs modulus of elasticity for the material of the wire.a)106 Pab)7 x 106 Pac)105 Pad)None of theseCorrect answer is option 'A'. Can you explain this answer?
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