1. What is Force Dimensional Formula?

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

Purpose: It helps in understanding the fundamental dimensions that make up the physical quantity of force.

2. Understanding the Components

The dimensional formula breaks down as:

Where:

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

Explanation: Force equals mass times acceleration, and acceleration has dimensions of length divided by time squared.

3. Importance of Dimensional Analysis

Details: Dimensional formulas help verify equations, convert units, and understand relationships between physical quantities.

4. Using the Calculator

Tips: Enter values for mass (kg), length (m), and time (s) to see how they contribute to the force dimensional formula.

5. Frequently Asked Questions (FAQ)

Q1: Why is time squared in the denominator?
A: Because acceleration (which is part of force) has units of m/s² - length divided by time squared.

Q2: What are the SI units for force?
A: The SI unit is Newton (N), which equals kg·m/s².

Q3: Can this be used for other force equations?
A: Yes, the dimensional formula remains the same whether calculating gravitational force, friction, etc.

Q4: How does this relate to work or energy?
A: Work (force × distance) has dimensional formula [M L² T⁻²].

Q5: What about other systems of units?
A: The dimensional formula remains the same, though the base units may differ (e.g., pounds, feet, seconds).