The adjacent graph shows the extension (∆l) of a wire of length λ m suspended from the top of a roof at one end and with a load W connected to the other end. If the cross-sectional area of the wire is 10-6 m2, calculate the Young's modulus of the material of the wire:
Correct answer: A. 2 x 10^11 λ N/m2
- A. 2 x 10^11 λ N/m2
- B. 2 x 10^-11 λ N/m2
- C. 3 x 10^12 λ N/m2
- D. 2 x 10^13 λ N/m2
Explanation
To calculate Young's modulus (Y), use the formula Y = Stress/Strain. Here, Stress = Force (F) / Area (A) and Strain = Extension (Δl) / Original Length (λ). From the graph, you get the values needed for these parameters:Stress = F/A = W / 10-6 m2 and Strain = Δl / λ.Insert these into the Young's modulus formula:Y = (W / 10-6) / (Δl / λ) = (W * λ) / (Δl * 10-6).Using the data, calculate to get Y = 2 × 1011 λ N/m2.Option A is correct because it accurately applies the formula and concepts. Options B, C, and D are incorrect due to miscalculations or misinterpretations of the data or formula.
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