1. What is Coefficient of Elasticity?

The coefficient of elasticity (Young's modulus) is a measure of the stiffness of a solid material. It defines the relationship between stress (force per unit area) and strain (proportional deformation) in a material in the linear elasticity regime of a uniaxial deformation.

2. Understanding Dimensional Formula

The dimensional formula for coefficient of elasticity is:

Where:

• \( M \) — Mass (fundamental dimension)
• \( L \) — Length (fundamental dimension)
• \( T \) — Time (fundamental dimension)

Explanation: This dimensional formula represents the physical dimensions of Young's modulus in terms of fundamental quantities.

3. Derivation of Dimensional Formula

Details: Young's modulus (E) = Stress/Strain = (Force/Area) / (ΔL/L). Since strain is dimensionless, [E] = [Force]/[Area] = [M L T⁻²]/[L²] = [M L⁻¹ T⁻²].

4. Physical Significance

Importance: The dimensional formula helps in verifying the correctness of physical equations, converting units between different systems, and understanding the fundamental nature of physical quantities.

5. Frequently Asked Questions (FAQ)

Q1: What are the SI units of coefficient of elasticity?
A: The SI unit is Pascal (Pa), which is equivalent to N/m² or kg/(m·s²).

Q2: Why is the dimensional formula important?
A: It ensures dimensional homogeneity in equations and helps in unit conversions between different measurement systems.

Q3: What does negative exponent in length dimension mean?
A: The L⁻¹ indicates that elasticity is inversely proportional to length dimension, representing force per unit area.

Q4: How does this relate to stress and strain?
A: Since stress has dimensions [M L⁻¹ T⁻²] and strain is dimensionless, elasticity coefficient shares the same dimensions as stress.

Q5: Can this dimensional formula be used for other elastic moduli?
A: Yes, bulk modulus and shear modulus also have the same dimensional formula [M L⁻¹ T⁻²] as they all represent stress-strain relationships.