Question

Young's modulus of a perfect rigid body is

• A. Zero
• B. Unity
• C. Infinity
• D. Between zero and unity

Answer 1

The Correct Option is C

Young's modulus is a measure of the stiffness of a material and is defined as the ratio of stress to strain. For a perfectly rigid body, there is no deformation under applied stress, implying that the strain is zero. Since Young's modulus is the ratio of stress to strain, for a perfectly rigid body, it would be infinite, as the strain approaches zero.

So, the correct answer is (C): Infinity

Answer 2

Young's modulus \( Y \) is defined as the ratio of stress to strain in a material. Mathematically: \[ Y = \frac{\text{Stress}}{\text{Strain}} = \frac{F/A}{\Delta L / L} \] where:
\( F \) is the force applied,
\( A \) is the cross-sectional area,
\( \Delta L \) is the change in length,
\( L \) is the original length.

For a perfect rigid body, no deformation occurs regardless of the applied force, meaning the strain is zero. Since strain is zero, and Young's modulus involves dividing by strain, this results in an infinite value for Young's modulus.

Thus, the Young's modulus for a perfect rigid body is infinite.