Question

The Young’s modulus of a perfectly rigid body is:

• A. unity
• B. zero
• C. infinity
• D. some finite non-zero constant

Hint:

For a perfectly rigid body, the strain is zero, resulting in an infinite Young’s modulus.

Answer 1

The Correct Option is C

Step 1: Young’s modulus definition.
Young's modulus \( Y \) is defined as the ratio of stress to strain. 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, and \( \Delta L \) is the change in length. Step 2: Perfectly rigid body.
In a perfectly rigid body, there is no deformation (i.e., \( \Delta L = 0 \)) when a force is applied. Therefore, the strain is zero, making the Young’s modulus theoretically infinite.
Final Answer: \[ \boxed{\infty} \]