The dimensional formula of **Energy** is

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

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

From the above formula, it’s clear that **the dimension of energy is 1, 2, -2**.

## Derivation of Dimensional Formula of Energy

We can derive this formula using the definition of energy.

In physics, we can define energy as the ability to do work. Hence, mathematically,

```
Energy = Work Done
```

We know that work is equal to force multiplied by displacement.

```
Work Done = Force * displacement
```

Hence, our formula becomes

```
Energy = Force * displacement
```

Also, **Force = mass * acceleration**. Hence,

```
Energy = mass * acceleration * displacement
```

We know

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

Therefore,

```
Energy = (mass * distance * displacement ) / time
```^{2}
Energy = (mass * distance * displacement * time^{-2} )

Dimensionally, we use

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

Hence, the dimensional equation of energy becomes **[ M L ^{2} T^{-2} ]**.

## Frequently Asked Questions

### 1. What is the dimensional formula of Kinetic Energy?

The dimensional equation of Kinetic Energy is:

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

**Derivation**

We know the formula of Kinetic Energy (KE):

```
KE = (1 / 2 ) mass * velocity
```^{2}

Here, **velocity = displacement / time**.

```
KE = (1 / 2) mass * ( displacement / time )
```^{2}
KE = (1 / 2) mass * displacement^{2} * time^{-2}

Hence, dimensionally,

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

### 2. What is the dimensional formula of Potential Energy?

The dimensional equation of Kinetic Energy is:

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

**Derivation**

We know the formula of Potential Energy (PE):

```
PE = mass * gravitational field * height
```

In terms of units, we can deduce

- mass into
**kilogram** - the gravitational field into
**meter / second**^{2} - height into
**meter**

So,

```
PE = kilogram * (meter / second
```^{2}) * meter
PE = kilogram * meter^{2} * second^{-2}

And, dimensionally, we represent

- kilogram as
**[M]** - meter as
**[L]** - second as
**[T]**

Hence, dimensionally, we can represent Potential Energy as **[ M ^{1} L^{2} T^{-2} ]**.

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