What is the Dimension of Force

Dimensional Formula of Force with its Derivation

In this article, we will find the dimension of Force

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:-

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Quiz on Dimensional Analysis

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

\([MLT^{-2}]\)

\([ML^{-2}T^{-2}]\)

\([M^{-1}L^{-1}]\)

\([ML^{-1}T^{-2}]\)

Question 1 of 5

2. The dimensions of impulse are equal to that of

pressure

force

angular momentum

linear momentum

Question 2 of 5

3. Which of the following is a dimensionless quantity

Quantity of heat

Stress

Specific Heat

Strain

Question 3 of 5

4. A unitless quantity

does not exist

always has nonzero dimensions

never has nonzero dimensions

may have a nonzero dimension

Question 4 of 5

5. The dimension of angular velocity is

\([MLT^{-2}]\)

\([M^0L^0T^{-1}]\)

\([M^2L^0T^{-1}]\)

\([ML^2T^{-2}]\)

Question 5 of 5

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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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