How to find the value of 'g' ?
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If we drop a body (say a stone) of mass m from a distance R from centre of the earth of mass M, then the force exerted by the earth on the body is given by the Universal Law of Gravitation as :
F = GMm/R 2 -------->(1)
Thus force I'd exerted by the earth produces acceleration in the stone due to which the stone moves downwards.
We also know that : F = ma
So, acceleration of stone, a = F/m --------->(2)
Putting value of F from eq. 1 in the above relation we get :
a = GMm/R 2 × m
or a = GM/R 2
The acceleration produced by the earth is known as acceleration due to gravity and represented by the symbol g. So, by writing g in place of a in above equation, we get :
g = GM/R 2
where G is gravitational constant
M is mass of the earth
R is the radius of earth
The the value :
g = (6.67 × 10 to the power -11 Nm 2/kg 2) × (6 ×10 to the power 24) / (6.64 × 10 to the power 6) square
Therefore g = 9.8m/s 2
(I did the rough work in my notebook and that was way too long so I can't write. The photo was also not uploading. )
F = GMm/R 2 -------->(1)
Thus force I'd exerted by the earth produces acceleration in the stone due to which the stone moves downwards.
We also know that : F = ma
So, acceleration of stone, a = F/m --------->(2)
Putting value of F from eq. 1 in the above relation we get :
a = GMm/R 2 × m
or a = GM/R 2
The acceleration produced by the earth is known as acceleration due to gravity and represented by the symbol g. So, by writing g in place of a in above equation, we get :
g = GM/R 2
where G is gravitational constant
M is mass of the earth
R is the radius of earth
The the value :
g = (6.67 × 10 to the power -11 Nm 2/kg 2) × (6 ×10 to the power 24) / (6.64 × 10 to the power 6) square
Therefore g = 9.8m/s 2
(I did the rough work in my notebook and that was way too long so I can't write. The photo was also not uploading. )
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