FREE FALL

We have learnt that the earth attracts
objects towards it. This is due to the
gravitational force. Whenever objects fall                        

                                                             

towards the earth under this force alone, we
say that the objects are in free fall. Is there
any change in the velocity of falling objects?
While falling, there is no change in the
direction of motion of the objects. But due to
the earth’s attraction, there will be a change
in the magnitude of the velocity. Any change
in velocity involves acceleration. Whenever an
object falls towards the earth, an acceleration
is involved. This acceleration is due to the
earth’s gravitational force. Therefore, this
acceleration is called the acceleration due to
the gravitational force of the earth (or
acceleration due to gravity). It is denoted by
g. The unit of g is the same as that of
acceleration, that is, m s–2.
We know from the second law of motion
that force is the product of mass and
acceleration. Let the mass of the stone in
activity be m. We already know that there
is acceleration involved in falling objects due
to the gravitational force and is denoted by g.
Therefore the magnitude of the gravitational
force F will be equal to the product of mass
and acceleration due to the gravitational
force, that is,
F = m g
m g
d
or G 2
M
g =
d

where M is the mass of the earth, and d is
the distance between the object and the earth.
Let an object be on or near the surface of
the earth. The distance d  will be
equal to R, the radius of the earth. Thus, for
objects on or near the surface of the earth,
G 2
M × m
mg =
R

G 2
M
g =
R

The earth is not a perfect sphere. As the
radius of the earth increases from the poles
to the equator, the value of g becomes greater
at the poles than at the equator.