define accerlation due to gravity.how it is vary along a height and depth drive mathematically
Answers
Definition: Acceleration due to gravity of an object is its rate of change of velocity due to the sole effect of the earth’s gravitational pull or gravity on that object that directs towards the centre of the earth.
Force of gravity acting on a body of mass m on the earth surface = F = GMm/R^2 ____________ (1)
Where R is the radius of the earth (considering it a homogenous sphere)
and M here is the total mass of earth concentrated at its centre. G is the gravitational constant.
Now, from Newton’s 2nd Law of Motion,
F = mg.___________________(2)
Just to recapitulate, as a body falls downwards it is continuously acted upon by a force of gravity. The body thus possesses an acceleration, called Acceleration Due to gravity(g).
From equation 1 and 2 we can write
mg = (GMm) / R^2
=> g = GM / R^2 _______________ (3)
Another expression of g here:
If mean density of earth is p then mass of the earth = M = volume X density = (4/3) Pi R^3 p
(Pi = 22/7)
g = G.( (4/3) Pi R^3 p) / R^2
g = (4/3) Pi R p G ________________ (4)