How to Prove that
M.g = GMm / r2
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^Well,
F = gMm/r^2 is gravitational force.
Also F = mg is the force experienced by a freely falling body due to action of gravity.
So mg = GMm/r^2 is the relation of forces of a freely falling body.
From here the value of g is calculated as follows.
g = GM/r^2
= 6.676208*10^-11 * 5.97 2* 10 ^24 / (6.4 * 10^6 )^2
( where Mass of earth (M) = 5.972 * 10^24 kg and radius of earth = 6400km =6 .4 * 10 ^ 6 m.)
= 9.8 m/s^2 approximately talking precised value of G ,M and r.
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Kurt Heckman, B.S. Mathematics, Eastern Nazarene College (1984)
Answered Feb 14
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Your formula is the Force of Gravity Equation
F=Gm1∗m2r2F=Gm1∗m2r2
where:
F is the gravitational force between the masses,
G is the gravitational constant(6.673×10−11 N·(m/kg)2),
m1 is the first mass,
m2 is the second mass, and
r is the distance between the centers of the masses.
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Santosh Khatiwada, studied at Ambition Academy Baneshore
Answered Feb 14
We know ,
Force (F) = mg …..(1)
Also ,
Force(F)= GMm/r^2 …….(2)
Now from equations (1)&(2) ,we get,
mg=GMm/r^2
where G= Universal gravitational constant
M = Mass of one substance
m= Mass of another substance
r= distance between them
g= acceleration due to gravity
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Bruno Coutinho, Ph.D. Physics, Northeastern University (2016)
Answered May 4
That equation is a very simple example of classic gravity.
mg , mass of an objectttimes acelaration of that same object is the ‘force’ acting in such object. This is general for objects at small speeds and with a constant mass.
The left side of the equation is the gravitional force caused by a body of mass M at distance r.
Because, in this case, the only force acting in that object is the gravitional force we get that equation.
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Divyansh Mani, studied Chemistry & Writing Poetry
Answered Feb 14
F=W
W=mg
But,
F=GMm/r²
Hence,mg=GMm/r²
It is a formula used for calculating Force of gravitation between 2 bodies,according to Newtonian Physics
Here,m =Mass of smaller body
M=Mass o larger body (Earth)
G=Gravitational Constant(6.67*10^-11 Nm²/kg²
g= Acceleration due to gravity
r= radius of earth
From this,
g=GM/r²
The value of g can be calculated by this.
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