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In this article, we will find the dimension of Universal Gravitational Constant
Dimensional formula for Universal Gravitational Constant is <\/p>\n\n\n\n
![\"dimension](\"https:\/\/physicscatalyst.com\/article\/wp-content\/uploads\/2019\/12\/dimension-of-universal-gravitational-constant.png\")
<\/figure><\/div>\n\n\n\n Where
M -> Mass
L-> Length
T -> Time.
We would now derive this dimensional formula. <\/p>\n\n\n\n
Derivation for expression of Dimension of Universal Gravitational Constant<\/h2>\n\n\n\n
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<\/p>\n\n\n\n
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
$F= m \\times a$ <\/p>\n\n\n\n
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= $[M^0 L^1T^{-1}]$ <\/p>\n\n\n\n
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}]$ <\/p>\n\n\n\n
Now from equation (1) , we can determine the dimension of Universal Gravitational constant as Try the free Quiz given below to check your knowledge of Dimension Analysis:- <\/p>\n\n\n\n
$ \\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<\/sup> kg?1<\/sup> s?2<\/sup> .<\/p>\n\n\n\n
\nQuiz on Dimensional Analysis<\/strong><\/span><\/h2>\n
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