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⚛️ Physics  ·  Mechanical Properties of Solids  ·  NEET & JEE

A composite rod is made of two equal-length segments, one of Youngs modulus Y1 and area A, and the other of Youngs modulus Y2 and the same area A, joined end to end and stretched by force F. The effective Youngs modulus of the composite rod is:

Answer: 2Y1Y2/(Y1 + Y2).

  • A (Y1 + Y2)/2
  • B 2Y1Y2/(Y1 + Y2)
  • C Y1Y2/(Y1+Y2)
  • D Y1 + Y2

Correct answer: B. 2Y1Y2/(Y1 + Y2)

Explanation: Equal-length segments under the same force act like springs in series; the harmonic-mean-like combination gives effective Y = 2Y1Y2/(Y1+Y2).

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.

Read the full Mechanical Properties of Solids notes →