The dimensional formula of Torque is

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

where **[M]**, **[L]**, and **[T]** are the fundamental quantities: **Mass**, **Length**, and **Time**.

From the above formula, we can derive the **dimensions of torque as (1, 2, -1)**.

## Derivation of Dimensional Formula of Torque

We can derive this formula using the definition of torque.

In physics, we can define torque as the tendency of a force to rotate a body about some axis. So, mathematically, torque is given as:

```
Torque = Force * lever arm
```

Here, **lever arm** is the **perpendicular distance** from the axis of rotation to the line drawn along the direction of the force applied. Hence, we can also say

```
Torque = Force * distance
```

We know that **Force = mass * acceleration**. Substituting the value of **Force** in the above formula, we get

```
Torque = mass * acceleration * distance
```

We know

- acceleration = speed / time
- speed = distance / time
- acceleration = distance / time
^{2}

Therefore,

```
Torque = ( mass * distance / time
```^{2} ) * distance
Torque = ( mass * distance^{2} ) / time^{2}
Torque = mass^{1} * distance^{2} * time^{-2}

Dimensionally, we use

**[M]**for mass**[L]**for distance and displacement**[T]**for time

Now the formula becomes

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

Hence, the **dimensional equation of torque is τ = [ M**^{1}** L**^{2}** T**^{-2}** ]**.

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