**Dimensional Formula of universal gravitational constant**

**Dimensional Formula of universal gravitational constant**

**with its Derivation**

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 m^{3} kg^{?1} s^{?2} .

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

**Quiz on Dimensional Analysis**

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