What is the dimension of Density

Dimensional Formula of Density

In this article, we will find the dimension of density
Dimensional formula for density is
$[M^1 L^{-3}]$
Where
M -> Mass
L -> Length

We would now derive this dimensional formula.

Derivation for expression of Dimension of Density

Density is defined as the  mass per unit Volume
$\rho= \frac {mass}{Volume} = \frac {m}{V}$

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

Now Dimension of Volume = $ [L^3]$
Hence Dimension of Density is given by
$\text {Dimension of Density}= \frac {[M^1]} {[L^3]} = [M^1 L^{-3}]$
Unit of Density  is $kg/m^3$

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. Choose the correct statement(s)

A dimensionally correct equation may be incorrect

A dimensionally correct equation may be correct

A dimensionally incorrect equation may be incorrect

A dimensionally incorrect equation may be correct

Question 1 of 5

2. The dimension of torque is

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

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

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

\([ML^3T^{-3}]\)

Question 2 of 5

3. The dimension of angular velocity is

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

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

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

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

Question 3 of 5

4. The dimensions of impulse are equal to that of

angular momentum

force

linear momentum

pressure

Question 4 of 5

5. The dimensions of universal gravitational constant are

\([M^{-1}L^{3}T^{-2}]\)

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

\([M^{-2}L^{3}T^{-2}]\)

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

Question 5 of 5

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Related Articles and references

1. New Simplified Physics by SL Arora : I highly recommend this book for class 11 Physics students. It is easy to understand with lots of solved problems.
2. Dimensional Analysis:- a very good website for physics concepts
3. Dimensional Formula of Work
4. Dimensional Formula of Spring constant
5. Dimension of Force

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