1. What Is The Dimensional Formula Of Coefficient Of Elasticity?

The dimensional formula of coefficient of elasticity (Young's modulus) is [ML⁻¹T⁻²]. This represents the fundamental physical dimensions of mass (M), length (L), and time (T) that define this physical quantity.

2. How Does The Calculator Work?

The calculator demonstrates the dimensional formula:

Where:

• \( M \) — Mass dimension
• \( L \) — Length dimension
• \( T \) — Time dimension
• \( E \) — Young's modulus (coefficient of elasticity)

Explanation: The dimensional formula shows that Young's modulus has dimensions of mass per unit length per time squared, derived from stress (force/area) divided by strain (dimensionless).

3. Importance Of Dimensional Analysis

Details: Dimensional analysis is crucial for verifying equations, converting units, and understanding the physical nature of quantities. It ensures dimensional homogeneity in physical equations.

4. Using The Calculator

Tips: Enter values for mass, length, and time to understand how these fundamental dimensions combine to form the dimensional formula of elasticity coefficient.

5. Frequently Asked Questions (FAQ)

Q1: What is Young's modulus?
A: Young's modulus is a measure of the stiffness of a solid material, defined as the ratio of stress to strain in the elastic region.

Q2: Why is the dimensional formula important?
A: It helps verify the correctness of physical equations and facilitates unit conversions between different measurement systems.

Q3: How is this dimensional formula derived?
A: From stress = force/area = [MLT⁻²]/[L²] = [ML⁻¹T⁻²], and strain being dimensionless, so E = stress/strain = [ML⁻¹T⁻²].

Q4: What are the SI units of coefficient of elasticity?
A: Pascals (Pa) or Newtons per square meter (N/m²), which are equivalent to kg/(m·s²).

Q5: Can dimensional formulas be used for calculations?
A: Primarily for verification and unit conversion, not for numerical calculations which require actual physical values.