1. What is Density Dimensional Formula?

Definition: The dimensional formula for density is [ρ] = M/L³, representing mass per unit volume.

Purpose: It helps in understanding the fundamental dimensions of density and performing dimensional analysis in physics.

2. Understanding the Formula

The dimensional formula is:

Where:

• \( [\rho] \) — Dimensional formula of density
• \( M \) — Mass dimension (kilograms)
• \( L \) — Length dimension (meters)

Explanation: Density is defined as mass divided by volume, and volume has dimensions of length cubed (L³).

3. Importance in Physics

Details: Dimensional formulas are crucial for:

• Checking the consistency of physical equations
• Deriving relationships between physical quantities
• Converting between unit systems
• Understanding fundamental properties of matter

4. Using the Calculator

Tips: Enter mass in kilograms and volume in cubic meters to calculate density in kg/m³. Both values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What are the SI units for density?
A: The SI unit is kilograms per cubic meter (kg/m³).

Q2: How does this differ from specific gravity?
A: Specific gravity is dimensionless as it's the ratio of a substance's density to water's density.

Q3: Can density have different units?
A: Yes, common alternatives include g/cm³ (1 g/cm³ = 1000 kg/m³) and lb/ft³.

Q4: Why is dimensional analysis important?
A: It helps verify equations and convert between measurement systems.

Q5: What's the density of water?
A: Pure water at 4°C has a density of exactly 1000 kg/m³.