1. What are Dimensional Formulas?

Definition: Dimensional formulas express physical quantities in terms of fundamental dimensions - Mass (M), Length (L), and Time (T).

Purpose: They help in checking the consistency of equations, converting units, and deriving relationships between physical quantities.

2. Understanding the Formulas

The dimensional formulas shown are:

Where:

• \( M \) — Mass (kilograms)
• \( L \) — Length (meters)
• \( T \) — Time (seconds)

Explanation:

• Pressure is force per unit area, hence the L⁻¹ term
• Force is mass times acceleration (L T⁻²), resulting in [M L T⁻²]

3. Importance of Dimensional Analysis

Details: Dimensional formulas are crucial for:

• Verifying the correctness of physical equations
• Deriving relationships between quantities
• Converting between unit systems
• Understanding the nature of physical quantities

4. Practical Applications

Examples:

• Checking if an equation like P = F/A is dimensionally consistent
• Deriving units of measurement for new quantities
• Understanding how changing units affects calculations

5. Frequently Asked Questions (FAQ)

Q1: Why does pressure have L⁻¹ in its dimensional formula?
A: Because pressure is force divided by area (L²), making the length dimension negative.

Q2: What are the SI units for these quantities?
A: Force is measured in Newtons (kg·m/s²), Pressure in Pascals (N/m² or kg/(m·s²)).

Q3: How would you derive the dimensional formula for force?
A: From Newton's second law: F = ma → [M] × [L T⁻²] = [M L T⁻²].

Q4: Can dimensional formulas be used for calculations?
A: They're primarily for analysis, not direct calculations, but help ensure calculations are dimensionally consistent.

Q5: What other fundamental dimensions exist?
A: Other systems may include electric current (I), temperature (Θ), and luminous intensity (J).