In our earlier lecture we studied how the
earth
attracts every object in this universe
towards the centre of the earth
with the force, known as gravity. Now
you would be surprised to know that this
phenomenon of attracting obejts
to its centre is not specific to just earth
in fact every object
attracts every other object in the
universe. Yes!
Every object attracts every other object
in the universe.
So the computer is attracting you, you
are attracting the fan
the table is attracting the chair and so on
and the force with which
the objects attract each other is known as
the gravitational force.
This phenomenon of every object 
attrcting every other object is stated
in the Universal in law of gravitation and is
proposed
by sir Issac Newton.
The universal law of gravitation states
that every object in the universe
attracts every other object with the
force
which is directly proportional
to the product of their masses
and universaly proportional to the square
of the distance between them.
So let's try and understand this law
mathematically.
so what this law is trying to state is
that if the we have two objects,
say A and B
the mass of A is m1 and mass of B is m2
and the distance between A and B is r
then A and B will attract each other
with the force known as the
gravitational force.
And this force is directly proportional
to
the product of in product of the masses
of A and B
that is
m1 into m2
further F
is inversely proportional to the square
of the distance between them.
that is one by
r square.
so F that is the force of attraction
between these two objects
is directly proportional to the product
of the masses m1 into m2
and in inversely proportional to the
squared off the distance between them,
that is one by r square.
So we have F is directly proportional to m1 into m2
and F is directly proportional to one by
r square.
Now combining these two we can write
F is directly proportional to m1 into m2
divided by r square.
Further we cann remove the proportionality
sign by
introducing a proportionality
constant.
So F is equal to G into
m2 into m2 divided by r square,
where G is known as the universal
gravitational constant,
Note that G is a constant here
G is independent of
the masses of the two objects and it is
also independent
of the distance between the two objects.
Now what is the SI unit of G ?
when F is equal G into
m1 into m2  divided by r square. We could
rearrange to get, G is
equal to
F
into
r sqare divided by
m1
into m2,
now the unit of force is
Newton and
the unit of r which is distance is
meters and the SI unit of mass
is kg,
go the SI unit of G would be
equal to
Newton (N)
into r sqare which would be
meter square
divided by
mass into mass that would be kg
into
kg,
so the SI unit of G is given as
Newton (N) meter square divided by
kg square.
Now what is the value of this
G, that is what is the value of these
universal
gravitational constant ?
If we have two objects A and B
of masses 1kg each
and if they're least at the unit
distance that is
one meter apart from each other then
what would be
the value of F
would be equal to
G into m1
which is one in this case, m2
which is one in this case divided by
r square which is one square in this case.
So what we get is G into one divided by one
is equal to G.
so F is equal to G,
hence
G or the universal
gravitational constant is numerically
equal to the force of gravitation
which exist between two objects
of unit masses kept
at a unit distance from each
other
and this has been found to be
6.67 into 10
into the power -11
and since we've just studied that the SI
unit
of G is Newton meter square per kg square,
so the value of G in SI system
is given as 6.67 into Newton meter square
10 to the power -11 into
per kg square,
now we can substitute the value of F in
F get the universal law of gravitation
in the mathematical form which states
that and is equal to
6.67 into 10 to the power of -11
into m1 into m2 divided by
r square, Newton
the unit of forces Newton's.
Now if all objects attract each other
then would be expect that this bat
would attract this ball and would
by vice versa
attract the bat in such a way that they
would come
close to each other, well,
Let's find out the force with which
these two attract each other,
so the mass of a typical bat is
approximately 1kg
the mass of a cricket ball
is approximately 160 grams,
for calculation purpose let
it equal to be 200 grams, so
this is equal to 200 grams
or equal to 0.2 kg
and let us assume that they at a unit
distance from each other
that is at a distance of one meter from
each other, so let us find
the gravitational force of attraction
between his bat
and this ball.
We know that the gravitational force of
attraction
is equal to 6.67 into 10 to
the ppower -11 into m1 into m2 divided by
r square.
Lets substitute the values here, we get
6.67 into
10 to thepower -11 into
mass of the ball which is 0.2
into mass of the bat which is which is 1
divided by r square the r is the
distance
we assumed it to be 1 meter so 1 square
and if we can create this further what
we would get
is if F is equal to this number
that is 0.1334
into 10
to the power 1,2,3,4,5,6,7,8,9,10
and minus
10
Newton (N), so how big is this force
So, with this force
the bat and the ball would take
approximately 400
years to cover that unit distance of 1
meter
and that four hundred years is when we
have ignored
the frictional force which would oppose
there
coming together.
So you can now understand how small
a value of a force is this
and that is why we don't see things
moving to each other.
So the universal law of gravitation
states
that every object in the universe attracts
every other object with the force which
is directly proportional
to the product of their masses and
inversely proportionalto
the square to the distance between them
and mathematically
we can write it as F is equal to 6.67
into 10 to the power -11 into
m1 into m2 divided by r square
where
m1 and m2 are the masses of the objects
and r is the distance between the objects.
