A wire has a diameter of 0.75 mm.It is stretched 0.2% of its original length when a mass of 5 kg is hung from it.What is the Young's modulus of the wire? A)1.4 $\times$ 10¹⁰N/m² B)5.6 $\times$ 10¹⁰N/m² C)1.7 $\times$ 10¹¹N/m² D)5.6 $\times$ 10⁸N/m² E)1.4 $\times$ 10⁸N/m²

Question

Quizplus · Accepted Answer

Young's modulus (Y) is calculated using the formula Y = (F/A) / (ΔL/L), where F is the force applied, A is the cross-sectional area of the wire, ΔL is the change in length, and L is the original length. Given that the diameter of the wire is 0.75 mm, the radius (r) is 0.375 mm or 0.000375 m. The cross-sectional area (A) = πr^2 = π(0.000375 m)^2. The force (F) applied by the mass is found using F = mg, where m is the mass and g is the acceleration due to gravity (approximately 9.8 m/s^2). Thus, F = 5 kg * 9.8 m/s^2 = 49 N. The strain (ΔL/L) is given as 0.2%, or 0.002. Plugging these values into the Young's modulus formula and solving gives a value close to 5.6 x 10^10 N/m^2, which matches choice B.

A Wire Has a Diameter of 0 ×\times× 1010 N/m2 B)5

A Wire Has a Diameter of 0 $\times$ 10¹⁰N/m²
B)5