ELASTICITY

Elasticity is a property of objects due to which they oppose any change made in them by a deforming force and attained their initial state as the deforming force is removed. These types of objects are called elastic but the objects which do not attain their initial state are called inelastic.

TERMINAL SPEED

When a body falls freely in a liquid, then following forces act on the body;
   i)  weight of body
  ii) upthrust of liquid
 iii) viscous force

When above forces balance eachother, then the body attains a constant speed, this speed is known as terminal speed.

ENERGY OF A FLOWING LIQUID

Flowing liquid has three types of energy;

Pressure Energy  If there is a pressure p on the surface area A of liquid and liquid covers a distance l, due to this , then
           pressure energy = pAl
pressure energy per unit volume = p

Kinetic energy  If mass m and volume V of a liquid is flowing with velocity v, then

kinetic energy per unit volume = dV²/2
where, d = density of liquid

Potential energy  If mass m of liquid is at a height h above the earth's surface, then potential energy is
                          = mgh 

EQUATION OF CONTINUITY

When a liquid is in streamline motion in a tube of non-cross sectional area, then at each point on the path of liquid, the product of cross sectional area and the velocity of liquid is constant.
             
                              Av = constant = A₁ v₁ = A₂ v₂

FLOWS OF FLUIDS

Streamline flow  It that flow of liquid in which every particle of the liquid follows exactly the path of its preceding particle and has the same velocity in magnitude and direction as that of its preceding particle while crossing through that point.

Laminar flow  It is that steady flow in which the liquid moves in the form of layers.

Turbulent flow  It is that flow of liquid in which a liquid moves with a velocity greater than its critical velocity.

Critical Velocity  It is that velocity of liquid flow upto which the flow of liquid is a streamlined and above which its flow becomes turbulent.

CRITICAL TEMPERATURE AND CRITICAL PRESSURE

Critical temperature is the temperature above which gas cannot be liquified.

Necessary pressure, to liquify the gas at critical temperature is called critical pressure.
                                 
Critical volume, V_c = 3b

Critical temperature, T_c = 8a/27Rb

Critical pressure,  P_c = a/27b²

CAPILLARITY

Capillary tube is a tube of very narrow bore. When a capillary tube is immersed in a liquid, then the liquid rises or falls in capillary above or below the free surface of liquid, this action is called capillarity.

ANGLE OF CONTACT

The angle between the tangent to the liquid surface and the tangent to the solid surface at the point of contact is known as angle of contact.
The angle of contact is always measured through the liquid.

- If angle of contact = 90, then
   liquid will wet the walls of the vessel.
   the level of liquid will be horizontal in the capillary

- If angle of contact < 90, then
    liquid will wet the walls of the vessel.
    liquid will rise in the capillary tube.
    level of liquid in capillary tube will be concave.

- If angle of contact > 90, then
    liquid will not wet the walls of the vessel.
    liquid will fall in the capillary tube.
    level of liquid in capillary tube will be convex.

EXCESS PRESSURE

The pressure on the concave side of the liquid surface is always greater than the pressure on the convex side. This difference of pressure is called as excess pressure.
- Excess pressure inside a liquid drop is given by
                             p = 2T/R
- Excess pressure inside a soap bubble is given by
                             p = 4T/R

SURFACE ENERGY

The potential energy of molecules in the surface of liquid is called the surface energy.
                      Surface energy = T * delta(A)

where, T = surface tension of liquid
 delta(A) = increase in surface area

A molecule in the surface of liquid possesses more potential energy than a molecule in the interior of liquid.     

SURFACE TENSION

It is a property by virtue of which the free surface of liquid at rest behaves like stretched membrane tending to contract so as to possess minimum surface area.
Surface tension is the force acting normally on unit length of imaginary line drawn on the surface of liquid. Its unit is N/m.
                    T = f/ l

Surface tension of a liquid is independent of area of the surface.
A steel needle may be made to float on the surface of liquid due to surface tension. 

INTERMOLECULAR FORCES

The forces between the molecules of the substances are called intermolecular forces. There are two types of intermolecular forces as given below;

a) Cohesive Forces : The intermolecular force of attraction acting between the molecules of same substance is called Cohesive Force.

b) Adhesive Force : The intermolecular force of attraction acting between the molecules of different substances is called Adhesive Force.

- The liquid for which cohesive force is larger than adhesive force, does not wet the walls of vessel, e.g, mercury does not wet the glass vessel.
- The liquid for which adhesive force is larger than cohesive force, wets the walls of vessel, e.g, water wets the glass vessel.

THRUST AND PRESSURE

The total force exerted by a liquid an any surface in contact with it is called Thrust.
The force acting perpendicularly on unit area of a surface is called pressure.
                                             Pressure = Force / Area
                                                        p = F/A
It is a scalar quantity. Its unit is Pascal (Pa).

LAWS OF FLOATATION

When a body is immersed in a liquid, then two forces act on it.
i) weight of the body (w, vertically downwards)
ii) upthrust (F, upwards)
     a) w > F i.e., weight of body is greater than upthrust of liquid, in this condition body will sink.
     b) w = F i.e., weight of body is equal to the upthrust of liquid, in this condition the body floats                with whole of its volume inside the liquid.
     c) w < F i.e., weight of body is less than upthrust of liquid, body will float with some of its part              outside the liquid.
     d) When a block of ice floats in a liquid having density greater than that of water, then the liquid             level rises when all the ice melts into water.
     e) If the density of liquid is less than that of water, then liquid level falls.

ARCHIMEDES PRINCIPLE

When a body, totally or partially, is immersed in liquid at rest, it appears lighter, this apparent loss of weight is equal to the weight of liquid displaced by the immersed part of the body.

Apparent weight  = actual weight - Upthrust
                             = mg(1 - p/d)

where, d = density of body
            p = density of liquid

Weight of plastic bag full of air is same as that of empty bag, as the upthrust is equal to the air filled in the bag.

HYDROSTATICS (FLUIDS AT REST)

The branch of physics that deals with the study of fluids at rest is called hydrostatics. It is also used to define the pressure which is exerted by a liquid which is at rest.

RELATIVE DENSITY

The relative density is defined as the ratio of the density of the substance to the density of water at 4 degree celsius. It is also called specific gravity.
Relative density has no unit.

BUOYANT FORCE OR BUOYANCY

It is an upward force acting on the body immersed in a liquid. It is equal to the weight of liquid displaced by the immersed part of the body.

BAROMETER

It is a device used to measure the atmospheric pressure. In this a glass tube open at one end and having a length of about a meter is filled with mercury remains in liquid state at room temperature.

                            Measured Pressure, p = pgh

p = density of mercury
h = height of the mercury column

ATMOSPHERIC PRESSURE

The pressure on the surface of the earth due to atmosphere of the earth is called atmospheric pressure.

PASCAL LAW

If the pressure at some point in a fluid is changed, there will be an equal change in pressure at any other point.

FLUID

Fluids are substances which begin to flow when the external force is applied.

LAWS OF LIQUID PRESSURE

i) The pressure inside a liquid is same at every point on the same horizontal plane.
ii) The pressure exerted by the liquid is normal to any surface with which the liquid is in contact.
iii) The pressure at any point within the liquid is independent of shape of liquid surface as well as the area of liquid surface.
iv) Centre of Pressure is that point of the body immersed in liquid at which the resultant liquid pressure acts.

MATTER

Matter is any substance which has mass and occupies space. Matter can exist in various state.

States Of  Matter
There are three types of states of matter;

SOLID Solids are substances in which intermolecular forces are so strong that the molecules or ions remain almos fixed at their equilibrium positions.

LIQUID Liquids are substances in which intermolecular forces are lesser compared to solid and their shape can be changed.

GASES In gases intermolecular forces are very small and their shape and volume can be easily changed.

Properties Of Matter

Mass Very common to all matters, mass does not change unless divided or removed to a body of matter.

Weight It depends in the attraction of the pull of gravity thus it changes from place to place.

Volume It occupies space and capacity.

ESCAPE VELOCITY

1. The minimum velocity of the body that should be given to the body to enable it to escape away from the earth's gravitational field is called escape velocity.

2. When the energy of a satellite is zero, then it escapes away from its orbit and its path becomes parabolical.

3. The value of escape velocity of a body does not depend on its mass.

4. The escape velocity of a body depends on the radius of planet from which it is projected.

5. Value of escape velocity does not depend on the angle and direction of projection.

PLANET

The heavenly body which revolves round the sun is called planet, e.g. the earth.

Kepler's Law's of Planetary Motion

Ist Law Every planet revolves around the sun in an elliptical orbit with the sun at one focus of the ellipse.

IInd Law The line joining the sun to the planet sweeps out equal interval of time i.e., areal velocity of radius vector joining the planet to the sun is constant;
                                         dA/dt = constant = L/2m

where L= angular moment of the planet about sun

IIIrd Law  The square of time period of revolution is directly proportional to the cube of average distance of the planet round the sun.
                                       

GRAVITATIONAL POTENTIAL ENERGY

The gravitational potential energy of body at a point is equal to work done in assembling the system of masses from the infinity to its present configuration.
The gravitational potential energy of masses m1 and m2 at a distance r;
                                   U = - Gm₁ m_{2  / r}

GRAVITATIONAL POTENTIAL

The gravitational potential at a point in gravitational field is equal to the work done in carrying a unit mass from infinity to that point without acceleration.
Gravitational Potential due to mass M at a distance r is;
                                             V = -GM/r

SI Unit is JKg^-1

GRAVITATIONAL FIELD

The space surrounding a material body in which attraction of the body can be experienced is called gravitational field.
Intensity of gravitational field. The intensity of gravitational field at a point is equal to the force acting on the unit mass at that point, is given by  GM/r2.

ACCELERATION DUE TO GRAVITY

The force of gravity acting on a body having unit mass placed on or near the surface of the earth is called acceleration due to gravity.
It is represented by 'g'.
                                   g = GM_{e /} R_e²

where M_e = mass of earth and  R_e = radius of earth

GRAVITATION

The phenomena of action of attractive forces between two bodies by virtue of their masses is known as Gravitation.

Newton's Law of Gravitation
"The force of attraction between two objects is directly proportional to the product of their masses and inversely proportional to the square of distance between them".

                                         F = Gm₁ m_{2 /} r²

where G = universal gravitational constant

The gravitational force between the two masses is independent of the presence of other objects and medium present between the two masses.

MOMENT OF INERTIA OF SOME REGULAR BODIES- PART V

THIN ROD

i.) About the mid point of the rod perpendicular to length
                            I= Ml2/12

ii.) About one end of the rod
                            I= Ml2/3

MOMENT OF INERTIA OF SOME REGULAR BODIES- PART IV

SOLID SPHERE

i.) About diameter
                   I= 2MR2/5

ii.) About Tangent
                   I = 7MR2/5

MOMENT OF INERTIA OF SOME REGULAR BODIES- PART III

HOLLOW CYLINDER

i.) About its geometrical axis
                 I= M(R₁² + R₂²)/2

ii.) About an axis passing through its CG and perpendicular to the length
                I= M(R₁² + R₂²)/4 + ML2/12

MOMENT OF INERTIA OF SOME REGULAR BODIES- PART II

SOLID CYLINDER

i.) About its geometrical axis
                I=MR2/2

ii.) About an axis passing through its CG and perpendicular to the length
                I= (ML2/12) + (MR2/4)

MOMENT OF INERTIA OF SOME REGULAR BODIES- PART VI

THIN CIRCULAR RING

i.) About diameter
                  I= MR2/2

ii.) About an axis passing through its CG of the ring and perpendicular to the plane of ring
                 I= MR2

iii.) About tangent
                 I= 3MR2/2

MOMENT OF INERTIA OF SOME REGULAR BODIES- PART I

CIRCULAR DISC

i.) About diameter
          I= MR2/4

ii.) About an axis passing through its CG and perpendicular to the plane of disc
          I= MR2/2

iii.) About any tangent (parallel to diameter)
          I= 5MR2/4

MOMENT OF INERTIA

Moment of inertia of a body with respect to an axis of rotation is the product of the mass(m) and the square of perpendicular distance from axis of rotation(r).
                            I= mr2

S.I unit is kgm2.

- Moment of inertia is that property due to which objects oppose any change in their state of rotatry motion.
- Moment of inertia of a body depends on the axis of rotation of the body.

COLLISION

In physics, a collision will take place if either of the two bodies come in physical contact with each other or even when the path of one body is affected by the force exerted due to the other.

i.) ELASTIC COLLISION
    a.) Momentum is conserved
    b.) Total energy is conserved
    c.) Kinetic energy is conserved
    d.) Forces involved are conservative in nature

ii.) INELASTIC COLLISION
     a.) Momentum is conserved
    b.) Total energy is conserved
    c.) Kinetic energy is not conserved
    d.) Forces involved are may be non-conservative in nature

CONSERVATIVE AND NON CONSERVATIVE FORCES

If the work done by the force in displacing an object depends only on the initial and final positions of the object and not on the nature of the path followed between the initial and final positions, such a force is known as conservative force. E.g; Gravitational Force etc.
If the work done by the force in displacing an object from one position to another depends upon the path between the two positions such a force is known as non-conservative force. E.g; Force of Friction etc.

STABILITY AND EQUILIBRIUM OF BODIES

The centre of mass of a body remains in equilibrium, if the total external force acting on the body is zero.
Stable Equilibrium  In this, body tries to regain its equilibrium after being slightly displaced.

Unstable Equilibrium  In this, when a body is slightly displaced it gets further displaced.

Neutral Equilibrium  In this body remains in equilibrium even after being slightly displaced.

FRICTION

When a body slides or rolls over another body or on a surface, then a force opposing the motion acts between those surfaces of the body which are in contact, this force is called force of friction.

Types of Friction
a.) Static Friction: The force of friction  that comes into play between two surfaces in contact before the actual motion starts, is called static friction.

b.) Limiting Friction: The maximum force of friction which comes into play before a body just begins to slide over the surface of another body, is called limiting friction.

c.) Kinetic Friction: When a body moves over another body, then the force of friction acting between two surfaces in contact with relative motion is called kinetic friction.

d.) Rolling Friction: When one body rolls over another body, then the frictional force acting between two is called rolling friction.

PSEUDO FORCE

To validate Newton's laws in non-inertial frame of reference, we have to apply a force mass times the acceleration and in opposite direction of the acceleration of the frame.
When a lift is going upward, the pseudo force will be downward and when lift is going down, the pseudo force will be upward and accordingly weight of a man standing on a weighing machine in the lift will change.

INERTIA

Inertia is the virtue of a body due to which it tries to retain its state. Inertia is of three types:

a.) Inertia of rest  If a body is in rest, then it will remain in rest until an external force is applied on it.

b.) Inertia of Motion   If a body is in motion, then it will remain in motion until an external force is applied on it.

c.) Inertia of Direction  The tendency of a body to change by itself its direction of motion is called inertia of direction.

FORCE

Force is a push or pull which can change the position of a body as required. Forces are of two types;

Balanced Forces:  If there are many forces acting on a body, but resultant of all of them is zero, then the forces are called balanced forces.

Unbalanced Forces: If the resultant of all the forces is not zero, then the forces are called unbalanced forces.

LAW OF PARALLELOGRAM OF FORCES

If two forces are acting on a point simultaneously, whose magnitudes and directions can be shown by two adjacent sides of parallelogram, then the magnitude and direction of resultant force will be shown by the diagonal which passes through the point of intersection of those sides.

CENTRIFUGAL FORCE

1.) The virtual force that balances the centripetal force in uniform circular motion is called centrifugal force.
2.) Centrifugal force, F_s, directed radially outward.
3.) Centrifugal force is not the real force but it arises due to acceleration of accelerating or rotating frame.

CENTRIPETAL FORCE

We know that there is an acceleration in uniform circular motion and acceleration always occurs due to some force. This force is called centripetal force.

                                                         F= mv²/r   or   F= mrw²

1.) Direction of centripetal force is always towards the centre.
2.) Uniform circular motion cannot occur without centripetal force.

CENTRIPETAL ACCELERATION

When a body executes uniform circular motion, then its speed remains same but direction goes on changing i.e., its velocity changes. That means there is an acceleration. This acceleration is known as centripetal acceleration.

                                                   a= v²/r   or   a= rw²

1.) Direction of centripetal acceleration is always towards the centre.

2.) Centripetal acceleration is always same in magnitude but its direction changes continuously.

ACCELERATION TIME GRAPH IN ONE DIMENSIONAL MOTION- PART II

Description:  If a body is moving with a constant increasing acceleration, then acceleration time graph is a straight line.

Feature of Graph:  The body is moving with a positive acceleration and slope of straight line makes an angle less than 90' always with time axis.

ACCELERATION TIME GRAPH IN ONE DIMENSIONAL MOTION- PART I

Description:  If a body is moving with a constant decreasing acceleration, then acceleration-time graph is a straight line.

Feature of Graph:  The body is moving with negative acceleration, and slope of straight line which makes an angle greater than 90' with time axis.

VEOCITY TIME GRAPH IN ONE DIMENSIONAL MOTION- PART IV

Description:  If a body is moving with constant acceleration, and its initial velocity is not zero, then velocity-time graph is a straight line not passing through the origin.

Feature of Graph:  The area enclosed by the velocity time graph with time axis represents the distance travelled by the body.

VEOCITY TIME GRAPH IN ONE DIMENSIONAL MOTION- PART III

Description:  If a body is moving with constant retardation, and its initial velocity is not zero, then the velocity-time graph is a straight line not passing through origin.

Feature of Graph:  The slope of this straight line with time axis makes an angle greater than 90'.

VEOCITY TIME GRAPH IN ONE DIMENSIONAL MOTION- PART II

Description:  If a body is moving with increasing acceleration, then the velocity-time graph is a curve with bend upwards.

Feature of Graph:  The slope of velocity-time graph increases with time.

VEOCITY TIME GRAPH IN ONE DIMENSIONAL MOTION- PART I

Description:  If a body is moving with decreasing acceleration, then velocity-time graph is a curve.

Feature of Graph:  The slope of velocity-time graph decreases with time.

DISPLACEMENT TIME GRAPH IN ONE DIMENSIONAL MOTION- PART V

Description:  If a body is moving with a constant velocity, then time-displacement graph will be a straight line, inclined to time axis.

Feature of Graph:  Greater is the slope of straight line, higher will be the velocity.

DISPLACEMENT TIME GRAPH IN ONE DIMENSIONAL MOTION- PART IV

Description: If a body is moving with a constant acceleration, then time-displacement graph is a curve with bend upwards.

Feature of Graph:  The slope of time-displacement curve increases with time.

DISPLACEMENT TIME GRAPH IN ONE DIMENSIONAL MOTION- PART III

Description:  If a body is moving with a constant retardation, the time-displacement graph represents a curve bend downwards.

Features of Graph:  The slope of time-displacement curve decreases with time.

DISPLACEMENT TIME GRAPH IN ONE DIMENSIONAL MOTION- PART II

Description:  If a body is moving with infinite velocity, then time-displacement curve is a straight line parallel to displacement axis.

Feature of Graph:  such motion of a body is never possible.

DISPLACEMENT TIME GRAPH IN ONE DIMENSIONAL MOTION- PART I

Description:  If a Body returns back towards the original point of reference while moving with uniform negative velocity, the displacement-time graph is an oblique straight line, making an angle greater than 90' with the time axis.

Main Feature of Graph:  The displacement of body decreases with time with respect to the reference point, till it becomes zero.

UNITS OF DISTANCE

Some Smaller Units of Distance:

    ·         1 cm = 10^-2 m

    ·         1 mm = 10^-3 m

    ·         1 micron = 10^-4 cm = 10^-6 m

    ·         1 nanometre = 10^-7 cm = 10^-9 m

    ·         1 angstrom = 10^-8  cm = 10^-10 m

    ·         1 fermi = 10^-13 cm = 10^-15 m 

b    

       Bigger Units of Distance:

  

     ·         1 light year = 9.46 * 10¹⁵ m

    ·         1 parsec = 3.08 * 10¹⁶ m = 3.26 light year

    ·         1 astronomical unit = 1.496 * 10¹¹ m

SYSTEMS OF UNITS

A system of units is a complete set of units including both fundamental and derived physical quantities. There are some such systems which are given below;

FPS: It is the British Engineering system of units which uses foot(ft), pound(lb), and second(s) as the fundamental units of length, mass and time respectively.

CGS: This is also known as Gaussian system of units which uses centimeter(cm), gram(g) and second(s) the fundamental units of length, mass and time respectively.

MKS: It uses metre(m), kilogram(kg) and second(s) as the fundamental units of length, mass and time respectively.

SI SYSTEM: This system contains seven fundamental units and two supplementary fundamental units.

PHYSICAL QUANTITIES

All quantities in terms of which laws of physics are expressed and which can be measured directly and indirectly are called Physical Quantities. They are of two types;

1. Fundamental Quantities: These are the quantities which are independent of each other.
    There are seven fundamental quanties;
a.) Time
b.) Electric Current
c.) Temperature
d.) Luminous Intensity
e.) Amount of substance

2. Derived Quantities: These are the quantities which can be derived from fundamental quantities.
    Example: Velocity, Acceleration, Momentum etc.