1. What is Coefficient of Elasticity?

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

2. Understanding Dimensional Formula

The dimensional formula represents the physical quantity in terms of fundamental dimensions:

Where:

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

Explanation: This formula shows that elasticity has dimensions of pressure or stress, which is force per unit area.

3. Dimensional Analysis of Elasticity

Derivation: Stress = Force/Area = (Mass × Acceleration)/Area = [M][L T⁻²]/[L²] = [M L⁻¹ T⁻²]

Since strain is dimensionless, the coefficient of elasticity (stress/strain) has the same dimensions as stress.

4. Using the Calculator

Tips: Enter the exponents for mass, length, and time dimensions. The calculator will generate the corresponding dimensional formula. For standard elasticity coefficient, use M=1, L=-1, T=-2.

5. Frequently Asked Questions (FAQ)

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

Q2: Why are the dimensions M L⁻¹ T⁻²?
A: Because elasticity represents stress (force/area), and force has dimensions M L T⁻² while area has L².

Q3: What is the physical significance of these dimensions?
A: They represent energy density - energy per unit volume, since work = force × distance.

Q4: How does this relate to other elastic constants?
A: Bulk modulus and shear modulus have the same dimensional formula as they all represent different types of stress-strain relationships.

Q5: Can dimensional analysis predict numerical values?
A: No, dimensional analysis only reveals the form of relationships between physical quantities, not numerical coefficients.