Page 2 - LN

F = ma

Free fall acceleration or acceleration due to gravity is represented by ‘g’.

F = mg ———- (2)

Using equation (1) and (2),

2
mg = GMm/R
2
g = GM/R ——– (3)
Where, M = mass of earth

R = radius of earth

Now the next that comes to mind is that we have already seen is ‘G’ i.e. Universal
Gravitational Constant. Its value remains same everywhere. But is it true for g? From

equation (3) we can see that g depends on the dimension of the body i.e. mass and
radius. Hence it will not be same everywhere. Also, as the acceleration remains

constant during free fall motion, so we can use equations of motion. We just must
replace value of acceleration in all the equation with g.

Factors affecting acceleration due to gravity:

 Shape of the earth: The earth is not perfectly spherical in shape. It is slightly
flattened at the poles and bulgy towards the equator. The value of g is

maximum (9.83 m/s ) at the poles as the polar radius is minimum, while it is
2
minimum (9.78 m/s ) at the equator as the equatorial radius is maximum.
2
 Altitude: As the height (h) above the earth’s surface increases, the value of g
decreases.

 Depth: As the depth below the earth’s surface increases, the value of g

decreases and finally it becomes zero at the center of the Earth.
 Mass of the planet- Acceleration due to gravity is directly proportional to the

mass of the planet.

 Radius of the planet- g is inversely proportional to the square of the radius.
NOTE:

 Acceleration due to gravity is independent of the mass of the object.

 Lighter and heavier objects fall at the same rate.