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# What is the dimension of Impulse

## Dimensional Formula of Impulse

with its Derivation

Dimensional formula for Impulse is

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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