The dimensional formula of Surface Tension is

**[ M**^{1}** L**^{0}** 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 work as (1, 0, -2)**.

## Derivation of Dimensional Formula of Surface Tension

We can derive this formula using the definition of surface tension.

In physics, we can define surface tension as the total energy needed to increase the unit surface area of a liquid. Suppose a force acts on a particular length, then mathematically,

```
Surface Tension (T) = Force / length
```

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

```
T = (mass * acceleration ) / length
```

We know

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

Therefore,

```
Surface Tension (T) = mass * (distance / time
```^{2} ) / length
T = (mass * distance) / (time^{2} * length)
T = mass^{1} * distance^{1} * time^{-2} * length^{-1}

Dimensionally, we use

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

Now the formula becomes

```
Surface Tension (T) = [M
```^{1}] * [L^{1}] * [T^{-2}] * [L^{-1}]
T = [M^{1}] * [T^{-2}]

Since the formula doesnâ€™t include the fundamental quantity **Length**, we can use **[L ^{0}]**, which is equal to

**1**.

```
Surface Tension (T) = [M
```^{1}] * [L^{0}] * [T^{-2}]

Surface Tension (T) = [M^{1}] * [L^{0}] * [T^{-2}]

Hence, the **dimensional equation of surface tension is T = [ M ^{1} L^{0} T^{-2} ]**.

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