A wire of diameter 0.20 mm stretches by 0.20% when a 6.28-N force is applied to it.What is Young's modulus for this wire? A)2.5 × 10¹⁰ Pa B)1.0 × 10¹¹ Pa C)2.5 × 10¹² Pa D)1.0 × 10¹² Pa

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Quizplus · Accepted Answer

Young's modulus (Y) is given by the formula Y = (F * L) / (A * ΔL), where F is the force applied, L is the original length, A is the cross-sectional area, and ΔL is the change in length. Given the diameter (d) is 0.20 mm or 0.20 x 10^-3 m, the radius (r) is 0.10 x 10^-3 m. The area (A) = πr^2 = π(0.10 x 10^-3)^2 m^2. The stretch (ΔL/L) is 0.20%, or 0.002 in decimal form. Rearranging the formula for Y gives Y = F / (A * (ΔL/L)). Substituting the given values and solving for Y yields a value close to 1.0 × 10^11 Pa, making option B correct.

A Wire of Diameter 0