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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Solids are compared through crystal structure, amorphous arrangement, elasticity, plastic deformation, stress, strain and Young’s modulus. Electrical behavior depends on available charge carriers and band structure, so conductors, insulators and semiconductors must be distinguished from mechanical properties such as strength, stiffness and brittleness.
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