Two wires of equal length and cross-section are suspended as shown. Their Young's moduli are Y₁ and Y₂ respectively. The equivalent Young's modulus would be:
Correct answer: C. Y₁Y₂ / (Y₁ + Y₂)
- A. Y₁ + Y₂
- B. Y₁ + Y₂ / 2
- C. Y₁Y₂ / (Y₁ + Y₂)
- D. under root Y₁Y₂
Explanation
The correct answer is Option B: 2(Y1Y2)/(Y1 + Y2). In ascenario where two wires are of equal length and cross-section, the effective or equivalent Young's modulus whenthey are arranged in series is calculated using the formulafor the harmonic mean of the two moduli. This accounts forthe distribution of stress and strain across both wires.Option A is incorrect because it implies a linear addition ofmoduli, which is applicable in parallel arrangements, notseries. Option C is incorrect because it reflects a division ofstress in a different context. Option D suggests averagingthe moduli, which does not apply here.
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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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