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# What is the Dimensional Formula of Power

## Dimensional Formula of Power

with its Derivation

Dimensional Formula for Power is given by

$[M^1 L^2 T^{-3}]$

Here
M denotes Mass
L denotes Length
T denotes Time

### Derivation for expression

Power is defined as work done per sec
$Power = \frac {\text{work done}}{Time}$
or
$P = \frac {W}{t}$
Now

Dimension of  Time= $[M^0 L^0 T^{1}]$

Dimension Formula of Work can be derived using work done formula
Work is defined as the cross product for Force  and displacement
$W= F.d$
Where d -> displacement
F -> Force applied
W-> Work done by the Force

So,
Now the dimension of displacement= $[L^1]$
Dimension of force is given by=$[M^1L^1T^{-2}]$

Now we know both the displacement and Force dimension , we can calculate the dimension of Work easily as

$\text {dimension of Work} = \text {dimension of Force} \times \text {dimension of displacement}$

$= [M^1L^1T^{-2}] \times [L^1] = [M^1L^2T^{-2}]$

Now that we know the dimension of work done and time

Therefore

$\text{Dimension of Power} = \frac {[M^1 L^2 T^{-2}]}{[M^0 L^0 T^{1}]}= [M^1 L^2 T^{-3}]$
is denoted by $P$

Unit of Power is watt

Try the free Quiz given below to check your knowledge of Dimension Analysis:-

#### Quiz on Dimensional Analysis

1. A dimensionless quantity

Question 1 of 5

2. Which of the following pair does not have the same dimensions

Question 2 of 5

3. Which of the following physical quantity as the dimension of $[ML^2T^{-3}]$

Question 3 of 5

4. Which of the following is a dimensionless quantity

Question 4 of 5

5. Choose the correct statement(s)

Question 5 of 5

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