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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:-
Quiz on Dimensional Analysis
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