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# What is the Dimension of Momentum

## Dimensional Formula of Momentum

with its Derivation

Dimensional formula for Momentum is

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

Where
M -> Mass

L -> Length

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

### Derivation for expression of Dimension of Momentum

Momentum is defined as the product for mass  and Velocity
$p= mv$
Where
m -> mass
v-> Velocity
p->Momentum

So,
Now the dimension of Mass= $[M^1]$
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 = $[L^1]$

Hence dimension of Velocity= $\frac {[L^1]}{[T^1]}=[M^0 L^1T^{-1}]$

So, Dimension of Momentum is given by

$\text {Dimension of Momentum} =[M^1] \times [M^0 L^1T^{-1}] = [M^1L^1T^{-1}]$

Unit of Momentum is Kg m/s and it is denoted by letter $p$

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

#### Quiz on Dimensional Analysis

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

Question 1 of 5

2. The dimensions of universal gravitational constant are

Question 2 of 5

3. The dimensions of impulse are equal to that of

Question 3 of 5

4. The dimension of torque is

Question 4 of 5

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

Question 5 of 5

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