Question

show that the value of g is equal to 9.8 metre per second square

Answer 1

g = MG/R^2, 

where g – Acceleration due to gravity 
M – mass of the Earth = 5.98 x 10^24 kg 
G – Universal gravitational constant = 6.673 x 10^-11 Nm^2kg^-2 
R – Radius of the Earth = 6.38 x 10^6 m 

g = (5.98 x 10^24 x 6.673 x 10^-11) / (6.38 x 10^6)^2 
g = (39.90454 x 10^13) / (40.7044 x 10^12) 
g = 0.98034954 x 10 
g = 9.8 m/s^2 

Answer 2

In a simple way the acceleration due to gravity of earth can be computed by

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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