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# What is the Dimension of Force

## Dimensional Formula of Force with its Derivation

Dimensional formula for is

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

Where
M -> Mass

L -> Length

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

### Derivation for expression of Dimension of

As per second laws of Newton law’s, Force is defined as the product of mass and acceleration
$F= ma$
Where m -> Mass of the body
a -> Acceleration of the body

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

Lets derive the dimension of Acceleration
Now
$a = \frac {\Delta v}{t}$
Now dimension of Velocity= $[M^0 L^1T^{-1}]$
dimension of Time = $[M^0 T^1]$
So dimension of Acceleration = $\frac {[M^0 L^1T^{-1}]}{ [M^0 T^1]}= [M^0 L^1T^{-2}]$
Hence Dimension of force is given by

$\text {Dimension of Force} =[M^1] \times [M^0 L^1T^{-2}] = [M^1L^1T^{-2}]$

Unit of Force is Newton

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

Question 2 of 5

3. The dimensions of impulse are equal to that of

Question 3 of 5

4. A unitless quantity

Question 4 of 5

5. The dimension of torque is

Question 5 of 5

#### Related Articles and references

1. Newton’s Law of Motion
2. Newton’s Second Law of Motion
3. Dimensional Analysis:- a very good website for physics concepts
4. Dimensional Formula of Spring constant
5. dimension of Density
6. dimension of frequency

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