derive an expression for acceleration due to gravity of earth taking M as the mass of the earth and R is the radius of the earth
Answers
Answer:
g = GM/R^2
Explanation:
Let us say that a mass m is on the surface of the Earth. Then the force between them will be,
F = GmM/R^2
Also, the Earth will attract the mass with a force equal to its weight which is equal to mg.
So, mg = GmM/R^2 [Dividing both sides by m]
g = GM/R^2
Answer:
Acceleration due to gravity is represented by g. The standard value of g on the surface of the earth at sea level is 9.8 m/s2.
To calculate the value of g, we should put the values of G, M and R
Where G=universal gravitational constant, G=6.7×10
–11
Nm
2
kg
−2
mass of the earth, M=6×10
24
kg,
and radius of the earth, R=6.4×10
6
m.
g=
R
2
GM
g=
(6×10
6
)
2
6.67×10
−11
×6×10
24
=9.8m/s
2
Thus, the value of acceleration due to gravity of the earth, g=9.8m/s
2
Also we know Weight in nothing but the force exerted by the earth with a value of acceleration =9.8m/s
2
Now at the poles the value of acceleration due to gravity is higher as compared to the equator as the constant value of
g depends on the radius of the earth which decreases when we come down from poles to the equator.
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