What is dimension of universal gravitational constant

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Dimensional Formula of universal gravitational constant

with its Derivation

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In this article, we will find the dimension of Universal Gravitational Constant
Dimensional formula for Universal Gravitational Constant is

Where
M -> Mass
L-> Length
T -> Time.
We would now derive this dimensional formula.

Derivation for expression of Dimension of Universal Gravitational Constant

The force of gravity between two masses is defined as
$F= \frac {Gm_1m_2}{r^2}$
or
$G= \frac {F r^2}{m_1 m_2}$ -(1)
Where
F -> Force
G ->Universal Gravitational Constant
r -> Distance
m -> Mass

Now Dimension of Mass is $[M^1]$
Dimension of Distance is given by $[L^2]$
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
Now dimension of Velocity= $[M^0 L^1T^{-1}]$

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 Universal Gravitational constant as
$ \text{Dimension of G} = \frac { [M^1L^1T^{-2}] \times [L^2]}{[M^2]}$
$=[ M^{-1}L^3T^{-2}] $
Unit of Universal Gravitational constant is m³ kg^?1 s^?2 .

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

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