A wire of radius 0.2 mm is extended by 0.5% of its length when supported by a load of 1.5 kg. Determ

JAMB Physics 2023 54 views

A wire of radius 0.2 mm is extended by 0.5% of its length when supported by a load of 1.5 kg. Determine the Young’s modulus for the material of the wire. [Take g = 10 ms-2]

  1. 2.4 x 10⁹ Nm⁻²
  2. 1.3 x 10¹⁰ Nm⁻²
  3. 2.4 x 10¹⁰ Nm⁻² ✓
  4. 1.3 x 10⁹ Nm⁻²

Explanation

Young’s modulus Y = (F/A)/(ΔL/L). Force F = mg = 1.5 × 10 = 15 N. Area A = πr² = π(0.0002)² = 1.256 × 10⁻⁷ m².

Stress = F/A = 15/(1.256 × 10⁻⁷) = 1.194 × 10⁸ N/m². Strain = 0.5% = 0.005.

Therefore Y = stress/strain = (1.194 × 10⁸)/0.005 = 2.4 × 10¹⁰ N/m². This value indicates the wire’s resistance to stretching.

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