1. Understand the Relationship
We know that force is related to mass and acceleration:
* F = ma
Where:
* F is force
* m is mass
* a is acceleration
2. Express Acceleration in Terms of Fundamental Quantities
Acceleration is the rate of change of velocity, and velocity is the rate of change of displacement:
* a = (change in velocity) / time = (change in displacement / time) / time
* a = L / T²
3. Substitute into the Force Equation
Substitute the expression for acceleration into the force equation:
* F = m * (L / T²)
4. Solve for Mass
Rearrange the equation to isolate mass (m):
* m = F * (T² / L)
5. Dimensional Formula
Therefore, the dimensional formula for mass in terms of force, length, and time is:
* [M] = [F] [T²] / [L]
This means that mass can be expressed as force multiplied by the square of time divided by length.
