It
is every day experience that bodies like a ball thrown vertically
upward comes back to the earth. Why does it happen so? We
are even today fascinated how planets move around the sun
and how various stars are there in their orbits or positions?
All this has been possible due to the force of attraction
between any two masses. Newton called it force of gravitation
and he formulated a law connecting the force and masses
of the two bodies involved. The interesting aspect of this
gravitational force is that it is always attractive whatever
may be the size of bodies.
8.4.1
Newton’s law of gravitation
On the basis of some observations, Newton found that the
force of gravitation is directly proportional to the product
of masses of the two bodies and inversely proportional to
the square of the distance between the bodies. Mathematically,
F = G (m1*m2) / r2
Where
G is called the universal gravitational constant. In S.I.
units where m is measured in kilogram, F in newton and r
in metre, G has a value 6.67 x 10-11 N m2/kg2.
At once we see that for appreciable value of force, masses
should be very large. The gravitational force due to earth
is also known as gravity.
8.4.2
Acceleration due to gravity
Stand at the roof top of a three or more storeyed building
with stones of different masses in your two hands and drop
these together (Be careful don’t hurt anyone). Ask
another person (an observer) to observe falling of the stones.
You will find that both the stones fall simultaneously.
The earth’s gravity accelerates the bricks down. Since
both reach ground together, this acceleration, called acceleration
due to gravity (g), is same for both pieces and is same
for any mass. That is ‘g’ is independent of the
mass of the freely falling body. Its value changes from
place to place on the Earth and it is 9.81 ms -2 at the
equator. Its value is maximum at the poles.
8.4.3
Mass and weight
We know that acceleration due to gravity varies with geographical
latitude and the gravitational force is an inverse square
of force i.e. Fµ 1/r2 . However, the ratio of the
gravitational force to the free fall acceleration for a
given body at any point on the Earth is a constant.
The
ratio F/g is a characteristic of a body and is known as
the mass of the body according to Newton’s second law
of motion. Thus, mass of a body is defined as the ratio
of the force of gravity acting on the body to the free fall
acceleration. m = F/g. Mass is a scalar quantity and is
measured in kilogram (kg). Mass is also defined as the matter
contained in the body. At a given place the value of acceleration
due to gravity is same for all masses-big or small. Hence
force of gravity is proportional to the mass of the body.
