The dimensional formula of force is

**[ M ^{1} L^{1} T^{-2} ]**

where, **[M]**, **[L]**, and **[T]** represent fundamental quantity **Mass**, **Length**, and **Time**.

Now, let’s see how we can derive this formula.

## How to calculate the 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 ) / Time
```^{2}
= Mass^{1} * Displacement^{1} * Time^{-2}

Dimensionally, we use

- [M] to represent mass,
- [L] for displacement
- and [T] for time

Now the above formula becomes

```
Force = [ M
```^{1}] * [L^{1}] * [T^{-2} ]

Force = [ M^{1}] * [L^{1}] * [T^{-2} ]

Hence, the dimensional formula of Force is [ M^{1} L^{1} T^{-2} ].

## Frequently Asked Questions

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