LONG SIGHTEDNESS OR HYPER METROPIA

SYMPTOMS
In HYPER METROPIA, a person can not see objects clearly which are near to him, but he can see clearly     distant objects
REASON
The reason for HYPER METROPIA is that either the focal length of the lens of eye is too long or the     eyeball is too short.
WHAT HAPPENS IN HYPER METROPIA
In HYPER METROPIA, light rays from a near object are focused behind the Retina.
CORRECTION OF DEFECT
This defect can be corrected by using a convex lens of suitable focal length
POWER OF LENS
Power of lens is defined as the reciprocal of the focal length of the lens in meters.
FORMULA:
Power = 1/f(in meter)
Unit of power of lens is Dioptre.
DIOPTRE
Dioptre is defined as the power of lens whose focal length is one meter
if f =1 meter then the power of the lens = 1 dioptre.

KINETIC MOLECULAR THEORY OF MATTER

KINETIC MOLECULAR THEORY OF MATTER
According to kinetic theory of matter:
Matter is made of very small particles called MOLECULES. These molecules are in a state of motion. They possess Kinetic Energy. Molecular motion may be translational , rotational or vibrational. These molecules attract each other. As the temperature of a substance is increased , its molecular speed is also increased and vice versa. If a substance is compressed , The K.E of its molecules increases and its temperature rises For latest information , free computer courses and high impact notes visit : www.citycollegiate.com
BROWNIAN MOTION
A famous scientist ROBERT BROWN observed that molecules of a substance are moved in ZIG ZAG path. Their motion is random. They collide with each other and move in a new direction after collision in ZIG ZAG fashion. This type of motion present in the molecules of matter is called "Brownian motion".
Brownian motion
ELASTICITY
The property of solid by virtue of which a solid body recovers its original shape after the removal of an applied force is called "ELASTICITY".
ELASTIC LIMIT
If applied force on a solid is gradually increased, a state is reached after which the material will not return to it original shape even after the removal of applied force. This limit is called "ELASTIC LIMIT". After elastic limit, material is permanently deformed. Different substances have different elastic limit.
STRESS
When a body is deformed, the internal force came into play per unit area to restore it to its original state is called "STRESS" OR "Stress is an opposing force expressed per unit area which resists any change in shape."
Stress is equal to the force per unit area. Mathematically:
or
Stress produces when a body is made to change in length, volume or Shape by the application of an external force

STATES OF EQUILIBRIUM

States of equilibrium
There are three states of equilibrium:
Stable equilibrium    Unstable equilibrium    Neutral equilibrium
Stable equilibrium
When the center of gravity of a body lies below point of suspension or support, the body is said to be in    STABLE EQUILIBRIUM. For example a book lying on a table is in stable equilibrium.
Explanation
A book lying on a horizontal surface is an example of stable equilibrium. If the book is lifted from one edge    and then allowed to fall, it will come back to its original position.    Other examples of stable equilibrium are bodies lying on the floor such as chair, table etc.
Reason of stability
When the book is lifted its center of gravity is raised . The line of action of weight passes through the    base of the book. A torque due to weight of the book brings it back to the original position.
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Unstable equilibrium
When the center of gravity of a body lies above the point of suspension or support, the body is said to    be in unstable equilibrium
Example
pencil standing on its point or a stick in vertically standing position.
Explanation:    If thin rod standing vertically is slightly disturbed from its position it will not come back to its original    position. This type of equilibrium is called unstable equilibrium, other example of unstable equilibrium are    vertically standing cylinder and funnel etc.
Reason of instability
when the rod is slightly disturbed its center of gravity is lowered . The line of action of its weight lies    outside the base of rod. The torque due to weight of the rod toppled it down.
Neutral equilibrium
When the center of gravity of a body lies at the point of suspension or support, the body is said to be in    neutral equilibrium. Example: rolling ball.
Explanation
If a ball is pushed slightly to roll, it will neither come back to its original nor it will roll forward rather it will    remain at rest. This type of equilibrium is called NEUTRAL EQUILIBRIUM.
Reason of neutral equilibrium
If the ball is rolled, its center of gravity is neither raised nor lowered. This means that its center of gravity    is at the same height as before.

DISTRIBUTIVE LAW FOR DOT PRODUCT

DISTRIBUTIVE LAW FOR DOT PRODUCT
According to distributive law for dot product:
	PROOF
	Consider three vectors , and .Here we will use geometric interpretation of dot product by drawing projection as shown below. First we obtain the sum of vectors  and by head to tail rule then we draw projection  and from the terminal point of vector respectively onto the direction of . The dot product  is equal to the projection of vector  onto the direction of  multiplied by the magnitude of. i.e.

MULTIPLICATION & DIVISION OF VECTOR BY A NUMBER (SCALAR)

MULTIPLICATION OF A VECTOR BY A SCALAR
When a vector is multiplied by a positive number (for example 2, 3 ,5, 60 unit etc.) or a scalar only its magnitude is changed but its direction remains the same as that of the original vector. If however a vector is multiplied by a negative number (for example -2, -3 ,-5, -60 unit etc.) or a scalar not only its magnitude is changed but its direction also reversed.
The product of a vector by a scalar quantity (m) follows the following rules:
	(m)  = (m) which is called commutative law of multiplication.
	m(n) = (mn) which is called associative law of multiplication .
	(m + n) = m+ n which is called distributive law of multiplication .
	DIVISION OF A VECTOR BY A SCALAR
	The division of a vector by a scalar number (n) involves the multiplication of the vector by the reciprocal of the number (n) which generates a new vector.
	Let n represents a number or scalar and m is its reciprocal then the new vector  is given by :
	where m = 1/n
	and its magnitude is given by:
	The direction of  is same as that of if (n) is a positive number.  The direction of  is opposite as that of if (n) is a negative number.

RESOLUTION OF VECTOR

DEFINITION
The process of splitting a vector into various parts or components is called "RESOLUTION OF VECTOR"
These parts of a vector may act in different directions and are called "components of vector".
	We can resolve a vector into a number of components .Generally there are three components of vector viz. Component along X-axis called x-component Component along Y-axis called Y-component Component along Z-axis called Z-component
	Here we will discuss only two components x-component & Y-component which are perpendicular to each other.These components are called rectangular components of vector.
	METHOD OF RESOLVING A VECTOR INTO RECTANGULAR COMPONENTS
	Consider a vector  acting at a point making an angle q with positive X-axis. Vector  is represented by a line OA.From point A draw a perpendicular AB on X-axis.Suppose OB and BA represents two vectors.Vector OA is parallel to X-axis and vector BA is parallel to Y-axis.Magnitude of these vectors are Vx and Vy respectively.By the method of head to tail we notice that the sum of these vectors is equal to vector.Thus Vx and Vy are the rectangular components of vector . Vx = Horizontal component of . Vy = Vertical component of .
	MAGNITUDE OF HORIZONTAL COMPONENT
	Consider right angled triangle DOAB
	MAGNITUDE OF VERTICAL COMPONENT
	Consider right angled triangle DOAB