Question

b. Prove that g=
GM/ R2

Taking G-6.67 x 10
11 Nm2 kg -2, M 6 kg and R

6.4 m. determine the value of acceleration due to gravity

of the earth.

Answer 1

From the universal law of gravitation we get,
Force between 2 bodies is equal to G×M×m/R^2
where G- universal gravitational constant.
M- Mass of the bigger body
m- Mass of the smaller body
R- Difference between the centers(C.O.G) of the 2 bodies.
But, we also know that the force or weight of an object ON EARTH is equal to m×g
where m- the mass if object
g- acceleration due to gravity on earth
So mg=GMm/R^2
therefore, g=GM/R^2

Calculating acceleration due to gravity of earth
Given- Mass of earth(M)- 6×10^24Kg
G- 6.67×10^-11
R- 6.4×10^6
thus, by putting in the values
g=GM/R^2
g=(6.67×10^-11)×(6×10^24)/(6.4×10^6)^2
and so, value of g at earth comes out to be approximately 9.81m/s^2

Answer 2

ANSWER :-
Using g = GM/R^2

Where G is Universal Gravitational Constant (6.67 * 10^-11 N-m^2/Kg^2)

M is Mass of earth (6*10^24 Kg)

R is Radius of earth (6.4*10^6 m)

By plugging in the respective values in the above expression

g = (6.67 * 10^-11 N-m^2/Kg^2 ) x (6*10^24 Kg) / (6.4*10^6 m)^2

After simplification we will get g around 9.8 m/ s^2.

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