Why is acceleration due to gravity constant?
Mass of the falling body cancels out because the force of gravity is directly proportional to the mass and the acceleration caused by that force is inversely proportional to the mass.
The force of gravity on a body of mass
The only data used in the calculation of
#G#is the universal constant of gravitation, value: #6.673*10^-11 (N*m^2)/"kg"^2#
#M_e#is the mass of the Earth: value #5.983*10^24 kg#
#R_e#is the radius of the Earth: value #6.37*10^6 m#
Newton"s 2nd Law tells us that trhe acceleration of that body of mass
I hope this helps,
As per Law of Universal Gravitation the force of attraction
#vecF_G =G (M_e*m)/r^2 hatr#.......(1)
Comparing modulii with the equation for Newton's Second Law of Motion
we get acceleration due to gravity, which is also called gravity, as
from above we see that when the body is located on the surface of the earth gravity is
#R_e#is radius of the earth.
As earth is not a perfect sphere, value of gravity
We also know that average radius of earth is
Therefore, for practical purposes we take acceleration due to gravity as a constant.