Let me ask you an interesting question.
Now you must have seen that when you
place a nail or any small iron object
in water it sinks immediately. But if you
have ever gone to the seaside you must
have seen big ships, heavy ships which float on water.
Now if it is common knowledge that a
heavier objects sinks in water but a lighter object floats, why is it that
this light pin is sinking but this
heavy object the ship is not sinking but
floating?
Find out the answer. Let us explain it on
the basis of Archimedes principle. But
first we are going to look at a very
interesting video.
In this video you will find that
plasticine dough is taken and moulded into a
flagship structure. As you can see, over
here this plasticine dough is floating. Now
observe what happens when the same
plasticine dough without any addition is
curled up to a ball and then it sinks. So
as you could see the same plasticine dough of
same mass floated when it shape was flat but
sunk when it was curled up into a ball.
Now when we consider the flotation or
sinking of any object, it is important
to remember that any object in a fluid
has two forces acting on it. There is the
downward force, that is, the weight of the
object and the upward force, that is, the
buoyant due to the liquid. So let us
find out in what case the object will
sink and in what case the object will
float.
So when the buoyant force is greater than
the weight of the object or in other
words the upward force is greater than
the downward force, the net force acting
on the body is in the upward direction
and thus the body will float.
The converse is also true. When buoyant force
is less than the weight of the object, the
object will move downwards. Why,
because the net force in that case will
be in the downward direction and thus
the object will sink. However, when the
buoyant force is equal to the weight of the
object, that is, the upward force and the
downward force cancel one another out,
the object will not move. It will remain
suspended.
So now let us see why a nail that is
kept in water sinks.
Firstly, we consider the weight of the
nail. The weight of the nail is nothing
but mass of the nail into acceleration
due to gravity. Now we have seen that
the density of any substance can be
expressed as mass divided by volume.
If I rearrange this equation, I can
write mass as density into volume.
Thus, mass is being written as volume into
density.
So if I now replace this equation in this
equation for weight, what will I get? I will
get weight of the nail is equal to volume 
of the nail
into density
of nail into
G, that is, the acceleration due to gravity.
Thus I get the equation volume into density
into G. Now if I symbolise this equation,
I can write it as V, which is the volume of
the nail  rho n, that is, the density of the nail
and G which is the acceleration due to
gravity. Now I have found out the weight
of the nail, that is, the force acting in
the downward direction. Now I have to
find out what the buoyant force or the force
acting in the upward direction is.
So according to Archimedes principle, the
buoyant force on the nail will be equal to
the weight of displaced water, that is,
the amount of water that is displaced by
the nail on submerging. The weight of that
water will give me the buoyant force
on the nail. So how can I find out the
weight of displaced water? The weight of
displaced water is equal to the mass of 
displaced water into acceleration due to
gravity.
Even in this case, I can write the mass as
volume
of displaced water
multiplied by
the density of
water that is displaced
into G, that is, acceleration due to gravity.
So I write it as volume of displaced water
into density into gravity and now I will
symbolise this equation. Now you might
be asking me that what the volume of
displaced water is. According to
Archimedes principle, the volume of the
nail that is kept in that volume will
displace an amount of water that has
equal volume.
Thus the volume of the nail and the
volume of displaced water will be equal
as given by Archimedes principle and we
had taken the volume of the nail as V.
So even in this case, the volume of
displaced water will be v.
So on symbolising this, I get V into rho w, 
that is, the density of water
into G,
that is, the acceleration due to gravity.
So even in this case, I have obtained an
expression for the buoyant force acting
on the nail.
So these other two forces acting on the
nail - the weight of the nail acting in
downward direction and the buoyant and
force acting in the upward direction. Now as
you can see
in the expression for weight and in
the expression for buoyant force
V and G are two common terms so they are not influencing the
magnitude in any way. What is influencing
the magnitude? That's right,
the density of nail
and the density of water. So it is quite
obvious that the density of nail which
is an iron object will be much much
greater than the density of water which
is a liquid.
Thus we can say that since the density of
nail is greater than the density of water,
the magnitude of the weight of the nail
will be much more than the magnitude of
the buoyant force. So in other words we can
say that the net downward force will
be much greater
because the downward force is more than
the upward force. So the net force is in
the downward direction and that is why the
nail sinks.
So the density of object immersed is more
than density of fluid and this is why
the object is sinking in the fluid and
not floating because the weight is more
than the buoyant force.
So now let us come to the question of
why a ship floats on water. A ship as we
know, is much heavier than a nail.
So firstly we consider a very
interesting video.
Over here an experiment has been done with
a toy ship.
You will notice this ship when placed in
water is displacing an amount of water whose
volume is equal to the volume of ship
that is submerged in water.
Now this ship is placed in a physical
balance. Once the ship has been placed in
physical balance, what is done is, where the
displaced water was collected, it is poured on the
other side of the physical balance in two
beakers and you will see that the level
of the physical balances becomes the
same, So what does this mean?
This means that the weight of water
displaced is greater than or equal to
the weight of the ship. If that physical
balance would have been allowed to stay
for a while, you would have seen that there
would have been a minute difference in
the two levels. So we can say that weight
of water displaced is greater than or
equal to the weight of the ship because 
that difference would have been due to
the fact that the waterside would have
been down, whereas the ship side would
have been comparatively in the upward
direction.
So since the weight of water is greater
than the weight of ship,
that is, the weight of water displaced. We can
see that the buoyant force which depends on
the amount of water displaced is greater
than the weight of the ship. So what does
this mean? This means that the net force
that is acting on the ship is in the upward
direction because the downward force
is less than the upward force
and it is due to this reason that the
ship floats on water and it does not
sink, whereas on the other hand we had
found that nail sunk in water because
the density of nail was greater than the
density of water. Now in the case of ship,
what happens is, most of the ship,
despite the fact that its body is
composed of metal,
it contains air inside or in other words
the ship is hollow. So the density of the
ship compared on a whole with that of water will be
much less and this is why we find the
ship floats on water.
