Buoyancy is an upward force exerted by a fluid that opposes the weight of an immersed object. Pressure increases with depth in a fluid and the pressure difference between the top and bottom of an object causes an upward buoyant force. According to Archimedes' principle, the magnitude of the buoyant force is equal to the weight of the fluid displaced by the submerged object. For an object to float, its density must be less than the fluid's density so the buoyant force exceeds the object's weight.

1. BUOYANCY
An upward force exerted by a fluid that opposes the
weight of an immersed object.

2. In science, buoyancy (upthrust) is an upward force exerted by a fluid
that opposes the weight of an immersed object. In a column of fluid,
pressure increases with depth as a result of the weight of the overlying
fluid. Thus the pressure at the bottom of a column of fluid is greater than
at the top of the column. Similarly, the pressure at the bottom of an
object submerged in a fluid is greater than at the top of the object.
This pressure difference results in a net upwards force on the object.
The magnitude of that force exerted is proportional to that pressure
difference, and (as explained by Archimedes' principle) is equivalent
to the weight of the fluid that would otherwise occupy the volume of
the object, i.e. the displaced fluid.
For this reason, an object whose density is greater than that of the fluid in
which it is submerged tends to sink. If the object is either less dense than
the liquid or is shaped appropriately (as in a boat), the force can keep
the object afloat. This can occur only in a reference frame which either
has a gravitational field or is accelerating due to a force other than gravity
defining a "downward" direction (that is, a non-inertial reference frame). In
a situation of fluid statics, the net upward buoyancy force is equal to the
magnitude of the weight of fluid displaced by the body.
The center of buoyancy of an object is the centroid of the displaced volume of fluid.

3. Archimedes' principle
Archimedes' principle is named after Archimedes of Syracuse, who first discovered this law in 212 B.C.[4] For
objects, floating and sunken, and in gases as well as liquids (i.e. a fluid), Archimedes' principle may be stated
thus in terms of forces:
with the clarifications that for a sunken object the volume of displaced fluid is the volume of the object, and
for a floating object on a liquid, the weight of the displaced liquid is the weight of the object.
More tersely: Buoyancy = weight of displaced fluid.
Archimedes' principle does not consider the surface tension (capillarity) acting on the body, but this
additional force modifies only the amount of fluid displaced, so the principle that Buoyancy = weight of
displaced fluid remains valid.
The weight of the displaced fluid is directly proportional to the volume of the displaced fluid (if the
surrounding fluid is of uniform density). In simple terms, the principle states that the buoyancy force on an
object is equal to the weight of the fluid displaced by the object, or the density of the fluid multiplied by the
submerged volume times the gravitational acceleration, g. Thus, among completely submerged objects with
equal masses, objects with greater volume have greater buoyancy. This is also known as upthrust.

4. Suppose a rock's weight is measured as 10 newtons when suspended by a string in a vacuum with gravity acting upon it. Suppose that when the rock is lowered into
water, it displaces water of weight 3 newtons. The force it then exerts on the string from which it hangs would be 10 newtons minus the 3 newtons of buoyancy force:
10 − 3 = 7 newtons. Buoyancy reduces the apparent weight of objects that have sunk completely to the sea floor. It is generally easier to lift an object up through the
water than it is to pull it out of the water.
Assuming Archimedes' principle to be reformulated as follows,
then inserted into the quotient of weights, which has been expanded by the mutual volume
yields the formula below. The density of the immersed object relative to the density of the fluid can easily be calculated without measuring any volumes.:
(This formula is used for example in describing the measuring principle of a dasymeter and of hydrostatic weighing.)
Example: If you drop wood into water, buoyancy will keep it afloat.
Example: A helium balloon in a moving car. During a period of increasing speed, the air mass inside the car moves in the direction opposite to the car's acceleration (i.e.,
towards the rear). The balloon is also pulled this way. However, because the balloon is buoyant relative to the air, it ends up being pushed "out of the way", and will
actually drift in the same direction as the car's acceleration (i.e., forward). If the car slows down, the same balloon will begin to drift backward. For the same reason, as
the car goes round a curve, the balloon will drift towards the inside of the curve.

5. Forces and equilibrium
This is the equation to calculate the pressure inside a fluid in equilibrium.The corresponding equilibrium equation
is: where f is the force density exerted by some outer field on the fluid, and σ is the Cauchy stress
tensor. In this case the stress tensor is proportional to the identity tensor: Here δij is the Kronecker
delta. Using this the above equation becomes:
Assuming the outer force field is conservative, that is it can be written as the negative gradient of some scalar valued
function: Then:
Therefore, the shape of the open surface of a fluid equals the equipotential plane of the applied outer conservative
force field. Let the z-axis point downward. In this case the field is gravity, so Φ = −ρfgz where g is the gravitational
acceleration, ρf is the mass density of the fluid.Taking the pressure as zero at the surface, where z is zero, the
constant will be zero, so the pressure inside the fluid, when it is subject to gravity, is
So pressure increases with depth below the surface of a liquid, as z denotes the distance from the surface of the
liquid into it. Any object with a non-zero vertical depth will have different pressures on its top and bottom, with the
pressure on the bottom being greater.This difference in pressure causes the upward buoyancy forces.
The buoyancy force exerted on a body can now be calculated easily, since the internal pressure of the fluid is known.
The force exerted on the body can be calculated by integrating the stress tensor over the surface of the body which is
in contact with the fluid: The surface integral can be transformed into a volume integral with the
help of the Gauss divergence theorem:
where V is the measure of the volume in contact with the fluid, that is the volume of the submerged part of the body.
Since the fluid doesn't exert force on the part of the body which is outside of it.

6. The magnitude of buoyancy force may be appreciated a bit more from the following argument. Consider any object of arbitrary shape and volume V surrounded by
a liquid.The force the liquid exerts on an object within the liquid is equal to the weight of the liquid with a volume equal to that of the object.This force is applied in
a direction opposite to gravitational force, that is of magnitude:
where ρf is the density of the fluid, Vdisp is the volume of the displaced body of liquid, and g is the gravitational acceleration at the location in question.
If this volume of liquid is replaced by a solid body of exactly the same shape, the force the liquid exerts on it must be exactly the same as above. In other words, the
"buoyancy force" on a submerged body is directed in the opposite direction to gravity and is equal in magnitude to
The net force on the object must be zero if it is to be a situation of fluid statics such that Archimedes principle is applicable, and is thus the sum of the buoyancy
force and the object's weight
If the buoyancy of an (unrestrained and unpowered) object exceeds its weight, it tends to rise. An object whose weight exceeds its buoyancy tends to sink.
Calculation of the upwards force on a submerged object during its accelerating period cannot be done by the Archimedes principle alone; it is necessary to
consider dynamics of an object involving buoyancy. Once it fully sinks to the floor of the fluid or rises to the surface and settles, Archimedes principle can be
applied alone. For a floating object, only the submerged volume displaces water. For a sunken object, the entire volume displaces water, and there will be an
additional force of reaction from the solid floor.
In order for Archimedes' principle to be used alone, the object in question must be in equilibrium (the sum of the forces on the object must be zero), therefore;
and therefore showing that the depth to which a floating object will sink, and the volume of fluid it will displace, is independent
of the gravitational field regardless of geographic location.
(Note: If the fluid in question is seawater, it will not have the same density (ρ) at every location. For this reason, a ship may display a Plimsoll line.)
It can be the case that forces other than just buoyancy and gravity come into play.This is the case if the object is restrained or if the object sinks to the solid floor.
An object which tends to float requires a tension restraint forceT in order to remain fully submerged.An object which tends to sink will eventually have a normal
force of constraint N exerted upon it by the solid floor.The constraint force can be tension in a spring scale measuring its weight in the fluid, and is how apparent
weight is defined.
If the object would otherwise float, the tension to restrain it fully submerged is:
When a sinking object settles on the solid floor, it experiences a normal force of:
Another possible formula for calculating buoyancy of an object is by finding the apparent weight of that particular object in the air (calculated in Newtons), and
apparent weight of that object in the water (in Newtons).To find the force of buoyancy acting on the object when in air, using this particular information, this
formula applies:
'Buoyancy force = weight of object in empty space − weight of object immersed in fluid'
The final result would be measured in Newtons.
Air's density is very small compared to most solids and liquids. For this reason, the weight of an object in air is approximately the same as its true weight in a
vacuum.The buoyancy of air is neglected for most objects during a measurement in air because the error is usually insignificant (typically less than 0.1% except for
objects of very low average density such as a balloon or light foam).

7. SIMPLIFIED MODEL
A simplified explanation for the integration of the pressure over the contact area may be stated as
follows:
Consider a cube immersed in a fluid with the upper surface horizontal.
The sides are identical in area, and have the same depth distribution, therefore they
also have the same pressure distribution, and consequently the same
total force resulting from hydrostatic pressure, exerted perpendicular to the plane
of the surface of each side.
There are two pairs of opposing sides, therefore the resultant horizontal forces
balance in both orthogonal directions, and the resultant force is zero.
The upward force on the cube is the pressure on the bottom surface
integrated over its area. The surface is at constant depth, so the pressure
is constant. Therefore, the integral of the pressure over the area of the horizontal
bottom surface of the cube is the hydrostatic pressure at that depth multiplied by
the area of the bottom surface.

8. Similarly, the downward force on the cube is the pressure on the top surface integrated over its area. The
surface is at constant depth, so the pressure is constant. Therefore, the integral of the pressure over the area of
the horizontal top surface of the cube is the hydrostatic pressure at that depth multiplied by the area of the top
surface.
As this is a cube, the top and bottom surfaces are identical in shape and area, and the pressure difference
between the top and bottom of the cube is directly proportional to the depth difference, and the resultant force
difference is exactly equal to the weight of the fluid that would occupy the volume of the cube in its absence.
This means that the resultant upward force on the cube is equal to the weight of the fluid that would fit into the
volume of the cube, and the downward force on the cube is its weight, in the absence of external forces.
This analogy is valid for variations in the size of the cube.
If two cubes are placed alongside each other with a face of each in contact, the pressures and
resultant forces on the sides or parts thereof in contact are balanced and may be disregarded,
as the contact surfaces are equal in shape, size and pressure distribution, therefore the buoyancy
of two cubes in contact is the sum of the buoyancies of each cube. This analogy can be extended
to an arbitrary number of cubes.
An object of any shape can be approximated as a group of cubes in contact with each other, and as
the size of the cube is decreased, the precision of the approximation increases. The limiting case for
infinitely small cubes is the exact equivalence.
Angled surfaces do not nullify the analogy as the resultant force can be split into orthogonal components
and each dealt with in the same way.

10. STABILITY
A FLOATING OBJECT IS STABLE IF IT TENDS TO RESTORE ITSELF TO AN EQUILIBRIUM POSITION
AFTER A SMALL DISPLACEMENT. FOR EXAMPLE, FLOATING OBJECTS WILL GENERALLY HAVE
VERTICAL STABILITY, AS IF THE OBJECT IS PUSHED DOWN SLIGHTLY, THIS WILL CREATE A GREATER
BUOYANCY FORCE, WHICH, UNBALANCED BY THE WEIGHT FORCE, WILL PUSH THE OBJECT BACK
UP.
ROTATIONAL STABILITY IS OF GREAT IMPORTANCE TO FLOATING VESSELS. GIVEN A SMALL
ANGULAR DISPLACEMENT, THE VESSEL MAY RETURN TO ITS ORIGINAL POSITION (STABLE), MOVE
AWAY FROM ITS ORIGINAL POSITION (UNSTABLE), OR REMAIN WHERE IT IS (NEUTRAL).
ROTATIONAL STABILITY DEPENDS ON THE RELATIVE LINES OF ACTION OF FORCES ON AN OBJECT.
THE UPWARD BUOYANCY FORCE ON AN OBJECT ACTS THROUGH THE CENTER OF BUOYANCY,
BEING THE CENTROID OF THE DISPLACED VOLUME OF FLUID. THE WEIGHT FORCE ON THE OBJECT
ACTS THROUGH ITS CENTER OF GRAVITY. A BUOYANT OBJECT WILL BE STABLE IF THE CENTER OF
GRAVITY IS BENEATH THE CENTER OF BUOYANCY BECAUSE ANY ANGULAR DISPLACEMENT WILL
THEN PRODUCE A 'RIGHTING MOMENT'.
THE STABILITY OF A BUOYANT OBJECT AT THE SURFACE IS MORE COMPLEX, AND IT MAY REMAIN
STABLE EVEN IF THE CENTRE OF GRAVITY IS ABOVE THE CENTRE OF BUOYANCY, PROVIDED THAT
WHEN DISTURBED FROM THE EQUILIBRIUM POSITION, THE CENTRE OF BUOYANCY MOVES FURTHER
TO THE SAME SIDE THAT THE CENTRE OF GRAVITY MOVES, THUS PROVIDING A POSITIVE RIGHTING
MOMENT. IF THIS OCCURS, THE FLOATING OBJECT IS SAID TO HAVE A POSITIVE METACENTRIC
HEIGHT. THIS SITUATION IS TYPICALLY VALID FOR A RANGE OF HEEL ANGLES, BEYOND WHICH THE
CENTRE OF BUOYANCY DOES NOT MOVE ENOUGH TO PROVIDE A POSITIVE RIGHTING MOMENT,

12. Density
If the weight of an object is less than the weight of the displaced
fluid when fully submerged, then the object has an average density
that is less than the fluid and when fully submerged will experience
a buoyancy force greater than its own weight. If the fluid has a
surface, such as water in a lake or the sea, the object will float and
settle at a level where it displaces the same weight of fluid as the
weight of the object. If the object is immersed in the fluid, such as
a submerged submarine or air in a balloon, it will tend to rise. If the
object has exactly the same density as the fluid, then its buoyancy
equals its weight. It will remain submerged in the fluid, but it will
neither sink nor float, although a disturbance in either direction will
cause it to drift away from its position. An object with a higher
average density than the fluid will never experience more buoyancy
than weight and it will sink. A ship will float even though it may be
made of steel (which is much denser than water), because it
encloses a volume of air (which is much less dense than water), and
the resulting shape has an average density less than that of the
water.

13. LIGHT
An important part of our lives

14.  When we are present in a dark room, we are not able to see any
object.
 Whenever we look a playground at late night, nothing is visible.
 What are the reasons behind it?
 Why can’t we see objects in dark places?
 LET US FIND OUT.

15. Light usually refers to visible light, which is electromagnetic
radiation that is visible to the human eye and is responsible for the
sense of sight. Visible light is usually defined as having a wavelength in
the range of 400nanometres (nm), or 400×10−9 m, to 700 nanometers –
between the infrared, with longer wavelengths and the ultraviolet, with
shorter wavelengths.
The main source of light on Earth is the Sun. Sunlight provides the
energy that green plants use to create sugars mostly in the form of
starches, which release energy into the living things that digest them.
This process of photosynthesis provides virtually all the energy used by
living things. Historically, another important source of light for humans
has been fire, from ancient campfires to modern kerosene lamps. With
the invention of electricity, electric lighting has all but replaced firelight.
THE REASON BEHIND IT.

16.  T H E A N G L E O F I N C I D E N C E ( D E N O T E D A S ( ∠ I ) ) A N D T H E
A N G L E O F R E F L E C T I O N ( D E N OT E D A S ( ∠ R ) ) A R E A L W A Y S
E Q U A L .
 T H E I N C I D E N T R A Y , T H E R E F L E C T E D R A Y A N D T H E
N O R M A L A T T H E P O I N T O F I N C I D E N C E A L L L I E O N T H E
S A M E P L A N E .
LAWS OF REFLECTION

17. 1ST LAW
•Fix a white sheet of paper on a drawing board or a table.
•Take a comb and close all its openings except one in the middle.
You can use a strip of black paper for this purpose.
• Hold the comb perpendicular to the sheet of paper. Throw light
from a torch through the opening of the comb from one side (Fig.
below).
•With slight adjustment of the torch and the comb you will see a
ray of light along the paper on the other side of the comb.
•Keep the comb and the torch steady. Place a strip of plane mirror
in the path of the light ray (Fig. 16.1). What do you observe?

18. 2ND LAW
•Perform previous activity again. This time use a sheet of
stiff paper or a chart paper.
•Let the sheet project a little beyond the edge of the
Table(Fig. below).
•Cut the projecting portion of the sheet in the middle. Look
at the reflected ray. Make sure that the reflected ray extends
to the projected portion of the paper.
•Bend that part of the projected portion on which the
reflected ray falls. Can you still see the reflected ray?
• Bring the paper back to the original position. Can you see
the reflected ray again?
• This infers the second law of reflection as the reflected ray
does not fall on the bended part of paper.

19. Care of the Eyes
 It is necessary that you take proper care of your eyes. If there is any problem you should go to an eye specialist. Have a
regular checkup.
 If advised, use suitable spectacles.
 Too little or too much light is bad for eyes. Insufficient light causes eyestrain and headaches. Too much light, like that of
the sun, a powerful lamp or a laser torch can injure the retina.
 Do not look at the sun or a powerful light directly.
 Never rub your eyes. If particles of dust go into your eyes, wash your eyes with clean water. If there is no improvement go
to a doctor.
 Wash your eyes frequently with clean water.
 Always read at the normal distance for vision. Do not read by bringing your book too close to your eyes or keeping it too
far.
 One should include in the diet components which have vitamin A. Raw carrots, broccoli and green vegetables (such as
spinach) and cod liver oil are rich in vitamin A. Eggs, milk, curd, cheese, butter and fruits such as papaya and mango are
also rich in vitamin A.

20. Animals have eyes shaped in different ways. Eyes of a crab are quite small but
they enable the crab to look all around. So, the crab can sense even if the enemy
approaches from behind. Butterfly has large eyes that seem to be made up of
thousands of little eyes (Fig. below). It can see not only in the
front and the sides but the back
as well.
A night bird (owl) can see very well
in the night but not during the
day. On the other hand, day light
birds (kite, eagle) can see well
during the day but not in the
night. The Owl has a large cornea
and a large pupil to allow more
light in its eye. Also, it has on its
retina a large number of rods and
only a few cones. The day birds
on the other hand, have more
cones and fewer rods.

21. Some persons, including children, can be visually handicapped. They have very limited vision to
see things. Some persons cannot see at all since birth. Some persons may lose their eyesight
because of a disease. Such persons try to identify things by touching and listening to voices
more carefully. They develop their other senses more sharply. However, additional resources can
enable them to develop their capabilities further.
Resources can be of two types : Non-optical aids and optical aids.
Non-optical aids include visual aids, tactual aids (using the sense of touch), auditory aids (using
the sense of hearing) and electronic aids. Visual aids, can magnify words, can provide suitable
intensity of light and material at proper distances. Tactual aids, including Braille writer slate and
stylus, help the visually challenged persons in taking notes, reading and writing. Auditory aids
include cassettes, tape recorders, talking books and other such devices. Electronic aids, such as
talking calculators, are also available for performing many computational tasks. Closed circuit
television, also an electronic aid, enlarges printed material with suitable contrast and
illumination. Nowadays, use of audio CDs and voice boxes with computers are also very helpful
for listening to and writing the desired text.
Optical aids include bifocal lenses, contact lenses, tinted lenses, magnifiers and telescopic aids.
While the lens combinations are used to rectify visual limitations, telescopic aids are available to
view chalkboard and class demonstrations.

22. The most popular resource for visually challenged persons is
known as Braille.
Louis Braille, himself a visually challenged person, developed
a system for visually challenged persons and published it in
1821.
Braille system has 63 dot patterns or characters. Each
character represents a letter, a combination of letters, a
common word or a grammatical sign. Dots are arranged in
cells of two vertical rows of three dots each.
The present system was adopted in 1932. There is Braille
code for common languages, mathematics and scientific
notation. Many Indian languages can be read using the
Braille system. Patterns of dots to represent some English
alphabets and some common words are shown below.
These patterns when embossed on
Braille sheets help visually
challenged to recognize words by
touching. To make them easier to
touch, the dots are raised slightly.

23. Visually challenged people learn the Braille system by beginning with
letters, then special characters and letter combinations. Methods depend
upon recognition by touching. Each character has to be memorized. Braille
texts can be produced by hand or by machine. Type writer - like devices and
printing machines have now been developed.
Some visually challenged Indians have great achievements to their
credit. Diwakar, a child prodigy has given amazing performances
as a singer.
Mr. Ravindra Jain, born completely visually challenged,
obtained his Sangeet Prabhakar degree from Allahabad.
He has shown his excellence as a lyricist, singer and music composer.
Mr. Lal Advani, himself visually challenged, established an Association for special
education and rehabilitation of disabled in India. Besides, he represented India on
Braille problems to UNESCO.
Helen A Keller, an American author and lecturer, is perhaps the most well-known and
inspiring visually challenged person. She lost her sight when she was
only 18 months old. But because of her resolve and courage she could complete her
graduation from a university. She wrote a number of books including
The Story of my Life (1903).