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⚛️ Physics  ·  Mechanical Properties of Solids  ·  NEET & JEE

A cube of side a is subjected to three mutually perpendicular equal stresses sigma on its faces (hydrostatic compression). If Youngs modulus is Y and Poissons ratio is sigma_p, the fractional decrease in volume in terms of bulk modulus B is given by ΔV/V = 3σ/Y multiplied by a factor. That factor, expressed using Poissons ratio, is:

Answer: (1 - 2σ_p).

  • A (1 - 2σ_p)
  • B (1 + 2σ_p)
  • C (1 - σ_p)
  • D 2σ_p

Correct answer: A. (1 - 2σ_p)

Explanation: For hydrostatic stress on a cube, the volumetric strain works out to ΔV/V = (3σ/Y)(1-2σ_p), connecting bulk modulus B = Y/[3(1-2σ_p)] to Youngs modulus and Poissons ratio.

Stress-Strain Curve for a Ductile Metal WireStrainStresselastic limityield pointUTS (max stress)fractureSlope of the straight (elastic) portion = Young's modulus Y; the curve beyond elastic limit shows permanent (plastic) deformation

A typical stress-strain curve: the initial straight line (Hooke's Law region, slope = Young's modulus) ends at the elastic limit; beyond the yield point, deformation becomes permanent, peaking at the ultimate tensile strength before the wire finally fractures.

Concept context

Stress, strain, Hookes law, and the elastic moduli that describe how solids deform and recover under load.

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