What is the Dimensional Formula of Power

Dimensional Formula of Power

with its Derivation

In this article, we will find the Dimensional Formula of Power

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:-

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Quiz on Dimensional Analysis

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1. Which of the following has the dimensions of pressure?

\([MLT^{-2}]\)

\([ML^{-1}T^{-2}]\)

\([M^{-1}L^{-1}]\)

\([ML^{-2}T^{-2}]\)

Question 1 of 5

2. A unitless quantity

never has nonzero dimensions

does not exist

always has nonzero dimensions

may have a nonzero dimension

Question 2 of 5

3. The dimension of angular velocity is

\([MLT^{-2}]\)

\([M^0L^0T^{-1}]\)

\([ML^2T^{-2}]\)

\([M^2L^0T^{-1}]\)

Question 3 of 5

4. The dimensions of impulse are equal to that of

pressure

linear momentum

force

angular momentum

Question 4 of 5

5. Which of the following is a dimensionless quantity

Stress

Quantity of heat

Specific Heat

Strain

Question 5 of 5

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