Question

The Young's modulus for perfectly rigid body is

• A. Zero
• B. 1 Pascal
• C. 3 Pascal
• D. Infinity

Answer 1

Answer:

D. Infinity

• Definition: Young's Modulus (E), also known as the modulus of elasticity, defines the relationship between stress and strain in a material within its elastic limit according to Hooke's Law (σ = Eε).
• Perfectly Rigid Body: A perfectly rigid body is a theoretical construct defined as a material that does not undergo any deformation, regardless of the magnitude of the applied load.
• Mathematical Derivation: Since the strain (ε) for a perfectly rigid body is zero for any finite stress (σ), the equation E = σ / ε leads to E = σ / 0.
• Result: Consequently, the Young's Modulus for a perfectly rigid body is mathematically defined as infinity (∞).
• Related Concepts:
  • For an ideal fluid, the Young's Modulus is zero.
  • Materials with a very high Young's Modulus, such as Diamond (~1200 GPa), are considered extremely stiff.
  • Structural steel typically has a Young's Modulus of approximately 200 GPa, which is a standard reference value in Strength of Materials exams.