Question

Prove g is approximately 10m/s2 on Earth by following these steps: Calculate the force of gravity between a falling object (for example an apple) and that of Earth. Use the symbol mo to represent the mass of the falling object. Now divide that force by the object’s mass to find the acceleration g of the object.

Answer 1

Weight of object = m0*g N

Force of gravity on object = F0 = G*Me*m0/(Re+h)^2

Since, Weight of object = F0

m0*g = G*Me*m0/(Re+h)^2

g = G*Me/(Re+h)^2

here, G = 6.67*10^-11

Me = mass of earth = 5.972*10^24 kg

Re = radius of earth = 6371 km = 6.371*10^6 m

h = height of object

Since, Re>>>h

So, Re+h   Re

then, g = G*Me/Re^2

g = (6.67*10^-11)*(5.972*10^24)/(6.371*10^6)^2

g = 9.81 m/s^2 10 m/s^2

g 10 m/s^2

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