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What is the dimension of Impulse


Dimensional Formula of Impulse

with its Derivation


In this article, we will find the dimension of Impulse

Dimensional formula for Impulse is

Dimension of Impulse

Where
M -> Mass

L -> Length

T-> Time
We would now derive this dimensional formula.

Derivation for expression of Dimension of Impulse

Impulse is defined as the product of Force and time. It is denoted by letter I
$I= F \times t$ -(1)
Where I = Impulse
F= Force
t=Time

Now dimension of Time is given by $[T]$
Lets derive the dimension of Force
Force is defined as product of Mass and acceleration
$F= m \times a$

Dimension of Mass is given by $[M]$
Dimension of Acceleration is derived as
$a= \frac {dv}{dt}$
Where v = velocity, t= time
Lets derive the dimension of Velocity
$v= \frac {dx}{dt}$
or
$v = \frac {d}{t}$
Now
Where
d-> displacement
t -> Time
Now Dimension of Displacement = $[L^1]$
Therefore, dimension of Velocity= $\frac {[L^1]}{[T^1]}=[M^0 L^1T^{-1}]$

So Dimension of Acceleration is given by
$\text{Dimension of Acceleration} =\frac {\text{dimension of velocity}}{\text {dimension of time}}$
$\text{Dimension of Acceleration} =\frac { [M^0 L^1T^{-1}] }{[T]}= [M^0L^1T^{-2}]$
Hence Dimension of Force will be
$ \text{Dimension of Force} = [M^1 ] \times [ M^0L^1T^{-2}] = [M^1L^1T^{-2}]$

Now from equation (1) , we can determine the dimension of Impulse as
$ \text{Dimension of Impulse} = (\text{Dimension of force}) \times (\text{Dimension of time}) $

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

Unit of Impulse is Kg m/s

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


Quiz on Dimensional Analysis


1. Which of the following is a dimensionless quantity

Question 1 of 5

2. A unitless quantity

Question 2 of 5

3. A dimensionless quantity

Question 3 of 5

4. Which of the following pair does not have similar dimensions

Question 4 of 5

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

Question 5 of 5


 


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Goody
1 year ago

This site is the best, plus their tests were amazing even though I got most of my answers wrong. It sharpened my thinking skills

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