The dimensional formula of force is
[ M1 L1 T-2 ]
where, [M], [L], and [T] represent fundamental quantity Mass, Length, and Time.
From this formula, we can say that the dimension of force is 1, 1, and -2 in terms of fundamental quantities Mass, Length, and Time.
Now, let’s see how we can derive this formula.
Derivation: Dimension Formula of Force
For this derivation, we need to revise some of the basic physics formulas.
| Quantity | Formula |
|---|---|
| Force (F) | Mass (m) * Acceleration (a) |
| Acceleration (a) | Velocity (v) / Time (T) |
| Velocity (v) | Displacement (D) / Time (T) |
Now, let’s use these formulas to find the dimension of the force.
Force = Mass * Acceleration
= Mass * (Velocity / Time) [using formula of acceleration]
= Mass * (Displacement / (Time * Time) ) [using formula of velocity]
= ( Mass * Displacement ) / Time2
= Mass1 * Displacement1 * Time-2
We know that dimensionally, we use [M] for mass [L] for displacement, and [T] for time.
With this in mind, our dimensional formula of force becomes
Force = [ M1 L1 T-2 ]
And finally,
Dimensions of Force = 1, 1, -2
1. How to find the SI unit of Force using the dimensional formula?
We know that the dimensional formula of force is [ M1 L1 T-2 ]. Now, let’s derive the unit from it.
The unit for
- [M], Mass is kg (kilogram)
- [L], length is m (meter)
- [T], time is s (second)
Now if we use these units for respective physical quantity,
Unit of Force = kg1 m1 s-2 = kg m s-2
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