A wire of length 3 m and radius 3 mm extends by 0.1 mm when a 50 kg mass is suspended from it. If Young's modulus is P×10¹¹ N m⁻² and g = 3π m s⁻², find P.
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Question

A wire of length 3 m and radius 3 mm extends by 0.1 mm when a 50 kg mass is suspended from it. If Young's modulus is P×10¹¹ N m⁻² and g = 3π m s⁻², find P.

G1 Physics · Accepted Answer

Young's modulus is Y = (stress)/(strain) = (F/A)/(ΔL/L) = FL/(AΔL). Here, F = mg = 50×3π N, L = 3 m, r = 3 mm = 3×10⁻³ m, A = πr² = π(3×10⁻³)², ΔL = 0.1 mm = 1×10⁻⁴ m. Therefore, Y = [50×3π×3] / [π(3×10⁻³)²(1×10⁻⁴)] = 5×10¹¹ N m⁻². Thus P = 5. Correct option: A.