1. What is the Dimensional Formula of Force?

Definition: The dimensional formula of force is [M L T⁻²], representing its dependence on mass (M), length (L), and time (T).

Purpose: This formula helps in understanding the fundamental dimensions that make up the physical quantity of force and allows for unit conversions and dimensional analysis.

2. How is the Dimensional Formula Derived?

The dimensional formula comes from Newton's second law of motion:

Where:

• \( F \) — Force (Newtons)
• \( m \) — Mass (kg) → dimension [M]
• \( a \) — Acceleration (m/s²) → dimensions [L T⁻²]

Explanation: Combining the dimensions of mass and acceleration gives the dimensional formula [M L T⁻²].

3. Importance of Dimensional Formula

Details: Dimensional formulas are crucial for:

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

4. Using the Calculator

Tips: Enter mass in kilograms and acceleration in meters per second squared to calculate the resulting force in Newtons.

5. Frequently Asked Questions (FAQ)

Q1: What are the base units of force in SI system?
A: The SI unit of force is Newton (N), which equals kg·m/s².

Q2: Why is time squared in the denominator?
A: Because acceleration is change in velocity (m/s) per time (s), making its units m/s².

Q3: Can this formula be used for other types of forces?
A: Yes, the dimensional formula applies to all types of forces (gravitational, electromagnetic, etc.).

Q4: How does this relate to other dimensional formulas?
A: Many formulas derive from force, like work (force × distance) with dimensions [M L² T⁻²].

Q5: What's the dimensional formula in other unit systems?
A: The dimensions remain [M L T⁻²] regardless of the unit system (SI, CGS, etc.).