C11. 1. Physical Quantity

 1. Physical Quantity

    Physics is the branch of science that deals with the natural laws in mathematical terms that determine the structure of the universe with reference to the matter and energy contained in it and their interactions. It is so broad that nature and behavior of atoms and subatomic particles and their constituent is studied under quantum mechanics and particle physics to large scale structure of universe, its origin, evolution with time is studied under cosmology and astrophysics. Physics intersects with many other branches of sciences such as biophysics and quantum chemistry, quantum computing, astronomy etc, due to which boundaries of physics has not been rigidly defined. Mathematics is the tool that is used by physicist to have the better understanding of natural phenomena. 

Matter:- Matter is any thing that has mass and occupies space which is composed of atom. It can exist in different sates like solid, liquid, gas, plasma etc. 

Physical quantity: - Those quantities which can be measured directly or indirectly is called physical quantity. Physical quantity obeys the natural laws which can be expressed interms of mathematical relations.

    A physical quantity has two parts i.e numerical values and unit. Numerical value or magnitude gives the quantitative idea of physical quantity. Unite gives idea about the physical quantity. There are two types of physical quantities. They are : 

i. Fundamental Physical quantity: The physical quantity which doe not depend on other physical quantity or the physical quantity which can not be express interms of other physical quantity and taken as stander is called fundamental physical quantities. 

    There are seven basic fundamental quantities. They are length, mass, time, temperature, electric current, luminous intensity and amount of substance and two supplementary fundamental quantities they are plane angle and solid angle. 

    The units of fundamental quantities are called fundamental units. For examples length(m), mass(Kg), time(s), electric current (A), luminous intensity(Cd), temperature(K), amount of substance (mol), plane angle (rad) and solid angle(sr).

ii. Derived physical quantities: The physical quantity which depend on fundamental physical quantity or can be expressed interms of fundamental physical quantity is called derived physical quantity. 

    The units of derived physical physical quantity is called derived units. For example: Velocity(m/s), density(Kg/m³), Specific heat capacity(J/Kg°C) etc. 

Measurement: Measurement is the process of comparing unknown quantity with known physical quantity. Measurement  is the root of science which guides us to learn the truth about the physical phenomena. Measurement is necessary for us in following ways:

i. It helps in selling and buying goods. 

ii. It helps in doing scientific experiments. 

iii. It helps in preparing goods and foods. 

iv. It helps in making medicines. 

v. It helps in constructing roads, buildings, bridges etc. 

Unit: To express any physical quantity, a unit and numerical value is necessary. So, a physical quantity is represented by a number followed by a unit. 

    Unit is defined as the standard quantity interms of which physical quantity of same kind is expressed or measured. 

                Unit = magnitude symbol

System of units: 

a. CGS System: The system of measurement in which length is measured in centimeter (cm), mass in gram(gm) and time in second(s). It is Franch system of measurement. 

b. FPS System: The system of measurement in which length is measured in foot (ft), mass in pound(lb) and time in second(s).It is the British system of measurement. 

c. MKS System: It is matric system of measurement. In this system length is measured in meter(m) in kilogram(Kg) and time in second (s). 

d. SI System: To establish uniformity in measurement all over the world, scientist held the Eleventh General conference on Weights and Measures in 1960 , France and approved seven basic quantities along with their units which is called SI unit. Later two supplementary quantities of angles were added to the system. 

List of SI units: 

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Heat and temperature

4. Heat and temperature

Heat is a form of energy that produces the sensation of warmth and flows from hot body to cold body.  It is produced due to the vibration of molecules. When molecules vibrate faster more heat is produced.
Matter is made up of molecules, these molecules contains energy. When substances are heated, molecules vibrate that increases the kinetic energy of the molecules. In other words when heat is supplied to an object, it increases the amplitude and frequency of vibration of molecules. These vibrating molecules contain kinetic energy called heat energy. Molecules are vibrating rapidly if the body is at high temperature.
The SI unit of heat energy is Joule (J). In CGS system, it is measured in calorie. One calorie is the quantity of heat required to raise the temperature of 1g of water through 1°C.
Heat also can be defined as the sum of the kinetic energy that the molecules of an object possess is called the heat energy of the object. Quantity of heat energy present in an object depends upon mass and average kinetic energy of the molecules. Quantity of heat is directly proportional to the:
i. Average kinetic of molecules of the body.
ii. Mass of a body i.e the total number of molecules that a body contains.
Heat energy has great many applications. It is used for cooking food, propelling and running vehicles, proper amount of heat from sun provides suitable place for living being on earth etc.

Effects of heat:
i. Increase in volume: When an object is heated, its size and volume increases.
ii. Chant in state: On heating, a solid converts into liquid, while liquid converts into vapour.
iii. Rise in temperature: When a body is heated its temperature increases.
iv. Physical change: When a body is heated, physical properties like colour changes.

Temperature: 
The temperature of a body is defined as the degree of hotness or coldness of a body or it can be defined as the average kinetic energy of molecules of the substance.
When two bodies at different temperature are placed in contact the heat flows from the body at higher temperature to the body at lower temperature. Temperature determines the direction of flow of heat energy from one body to another when these are in contact with each other. Thermometer is used to measure the temperature of an object. 

Thermometer: 

The instrument that is used to measure the temperature is called thermometer and the branch of science related to measurement of temperature of a body is called thermometery. There are different types of thermometer, they are liquid thermometer, gas thermometer, resistance thermometer, radiation thermometer, vapour thermometer etc.  

Liquid thermometer are based on the principle of change in volume of a liquid with change in temperature. Mercury and alcohol thermometers are based on this principle. 

Differences between heat and temperature: 

S.no	Heat	Temperature
1	Heat is a form of energy which gives us the sensation of warmth.	It is the degree of hotness or coldness of a body.
2	It is measured in calorie or joule.	It is measured in °C, K etc.
3	Heat flows from a body at higher temperature to a body at lower temperature.	The temperature of two bodies gives the direction of flow of heat.
4	It is the total KE of all the molecules of a substance.	It is the average KE of the molecules.
5.	It is measured by Calorimeter.	It is measured by the thermometer.
6.	It is cause of temperature.	It is effect of heat.

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Energy

Energy: 



Energy is defined as the capacity to do work. Energy is a scalar quantity. The SI unit of energy is joule (J) and erg in CGS system. The amount of energy produced by a body is equal to the amount of work it can do when the energy is released. In nature there exists different forms of energy like mechanical energy, heat energy, light energy, geothermal energy, nuclear energy, tidal energy, wind energy, chemical energy, electrical energy etc.
One joule of energy is the amount of energy which can move an object of weight 1N through 1 meter.
The sun radiates about 27 × 10²³ Kw (or 4×10^26 J/s) of energy per second and earth receives 1.4 Kw of energy per square meter from the sun. Sun is the major source of energy for us  because other form of energy are transformed from the solar energy either directly or indirectly. Energy is produced in the form of heat and light in sun by thermonuclear fusion reaction of hydrogen atoms. Solar energy is the renewable source of energy and it can be used for longer duration.

Law of conservation of energy: 
Law of conservation of energy states that "Energy can neither be created nor be destroyed by it can only be transformed from one form to another.

Sources of energy: 

i. Primary sources: The sources of energy from which we can obtain energy in natural form are called primary sources. Example: wind energy, solar energy, hydro energy, etc.

ii. Secondary sources: The sources of energy which are obtained after modification from the natural form is called secondary sources of energy. Examples: mineral oil, tidal energy etc.

Types of energy: 

i. Renewal source of energy: The sources of energy which can never be used fully are called can be renewed by the natural process are called renewal source of energy. They do not exhaust even after the regular use in a long period of time. E.g: Electricity, wind, geothermal energy, solar energy etc.

a. Solar energy: The energy that is obtained from sun is called solar energy. Solar energy is the best source of energy for all living beings on earth.

ii. Non-renewable source of energy: The sources of energy which can exhaust if once used up fully are called non-renewal source of energy. It takes long period of time to form again. Eg. petroleum oil, coal, natural gas etc.

Difference between renewable and non-renewable source of energy: 

Renewable source of energy	Non-renewable source of energy
1. The source of energy which can never be used up fully and renewed by natural process.	1. The source of energy which exhaust once it is used up fully.
2. They do not get exhausted even if used regularly.	2. They may exhausted due the regular use.
3. Wind energy, solar energy, tidal energy are renewable sources.	3. Petrol, coal and natural gas are the non-renewable source of energy.

Forms of energy and their uses: 
i. Mechanical energy: Mechanical energy is defined as the energy possessed by a moving body or the body resting at a certain place. There are two types of mechanical energy. They are:
   a. Kinetic energy: The energy possessed of a body by virtue of its motion is called kinetic energy. It is written as KE in short. Examples: energy of flowing water, energy of blowing air, energy of a rolling stone, energy of moving vehicles, etc. Let us consider a body with mass 'm' initially at rest is moving with an acceleration 'a', the final velocity of the body moving after certain distance 's' be 'v'. According to the equation of motion:

${{v}^{2}}-{{u}^{2}}=2as$
${{v}^{2}}=0+2as$  [since u=0]
$s=\frac{{{v}^{2}}}{2a}$

Again, KE = work done
                 = $F\times s$
                 = $ma\times \frac{{{v}^{2}}}{2a}$  [Since F = ma and $s=\frac{{{v}^{2}}}{2a}$]
Therefore, KE = $\frac{1}{2}m{{v}^{2}}$
From above equation it is found that KE of an object is directly proportional to the mass and the square of the velocity.

   b. Potential energy: The energy of a body by virtue of its position or configuration is called potential energy. Example: stretched rubber, water stored in a dam, compressed spring etc. In other words when work is done on a body, potential energy is gained i.e the potential energy gained is equal to work done on the body.
If  a body of mass 'm' when it is raised above the ground at certain height 'h' against the gravity, it tendency to fall back to the ground.  The potential energy of the body is equal to the work done in taking the object to height 'h'. Then,
Work done = F × h
                  = mg × h  [f = ma]
Potential energy (PE) = work done in moving the object to the height h.
                                   = mgh.

ii. Nuclear energy: The large amount of energy obtained after fusion or fission of nucleus of an atom or atoms is called nuclear energy.
       a. Nuclear fusion reaction: The reaction in which lighter nuclei fuse together to form a heavy nucleus with release of large amount of energy. The reaction that occur in sun is thermonuclear fusion reaction. Thermonuclear fusion reaction is a process in which two or more nuclei of smaller atoms fuse together to form a heavier atom under high pressure and temperature with the release of huge amount of energy. The reaction that occurs in sun is shown below:

${}_{1}{{H}^{1}}+{}_{1}{{H}^{1}}\xrightarrow{\text{High pressure and themprature}}{}_{1}{{H}^{2}}+{}_{1}{{e}^{0}}+\gamma (energy)$

${}_{1}{{H}^{2}}+{}_{1}{{H}^{1}}\xrightarrow{\text{High pressure and themprature}}{}_{2}H{{e}^{3}}+\gamma (energy)$

${}_{1}{{H}^{2}}+{}_{1}{{H}^{2}}\xrightarrow{\text{High pressure and themprature}}{}_{2}H{{e}^{4}}+\gamma (energy)$

${}_{1}{{H}^{2}}+{}_{1}{{H}^{3}}\xrightarrow{\text{High pressure and themprature}}{}_{2}H{{e}^{4}}+{}_{0}{{n}^{1}}+\gamma (energy)$
${}_{2}H{{e}^{3}}+{}_{2}H{{e}^{3}}\xrightarrow{\text{High pressure and themprature}}{}_{2}H{{e}^{4}}+{}_{1}{{H}^{1}}+{}_{1}{{H}^{1}}+\gamma (energy)$
In short,
$_{1}{{H}^{2}}{{+}_{1}}{{H}^{3}}{{\xrightarrow{\text{High pressure and themprature}}}_{2}}H{{e}^{4}}{{+}_{0}}{{n}^{1}}+\gamma (energy)$
Where,
\[_{1}{{H}^{1}}=\text{Protium,}{{\text{ }}_{1}}{{H}^{2}}=\text{Deuterium, }{}_{1}{{H}^{3}}=\text{Tritium,}{{\text{ }}_{1}}{{e}^{0}}=\text{Positorn,}{{\text{ }}_{0}}{{n}^{1}}\text{= neutron }\]
      b. Nuclear fission reaction: Nuclear fission reaction is the type of reaction in which heavier nucleon disintegrates into lighter fragments with the release of large amount of reaction. With the help of this reaction atomic bomb are made. The nuclear fission reaction of uranium atom is shown below:
$_{92}{{U}^{235}}{{+}_{0}}{{n}^{1}}{{\xrightarrow{{}}}_{56}}B{{a}^{141}}+{}_{36}K{{r}^{92}}+{{3}_{0}}{{n}^{1}}+\gamma (energy)$

iii. Geothermal energy:The heat energy present inside the earth's interior is called geothermal energy. The temperature inside the earth is about 5000°C to 6000°C. When the underground water comes in contact with this huge temperature it changes into steam or hot water. The steam and the hot water is pumped to the earth surface and used to rotate turbine to produce electricity. It is also used to keep house warm.

iv. Hydro-power: The energy that is obtained from the potential and kinetic energy of water is called hydro-power. Hydroelectric energy is the energy generated with the help of water. The water collected in dam or reservoir is made to fall from a certain height through a tunnel or pipe so that the force of falling water turns the turbine which drives the electric generator. With the help of coil and magnetic field electricity is produced. It is the best eco-friendly source of energy. There is wide used of electrical energy because it can be transformed into different other form of energy and apply for different purposes.
Nepal has high potentiality of hydro-power because most of the rivers in Nepal flow from high altitudes with high speed. Nepal has the potentiality of generating About 83000 MW of hydroelectric power. Only few thousands Mega watts of electricity has been produced until now. This clean energy source is boon to our country which boost up the economy if we able to harvest all of the hydroelectric energy.

v. Fossil fuel: Fossil fuel are the energy rich organic materials like oil, coal, natural gas, petroleum etc. which are formed from the dead remaining of plants and animals buried under earth's crust millions years ago. After decomposition the dead remaining turns into fossil fuel which are being used by human nowadays. 

vi. Coal : Coal is defined as an organic sedimentary rock that forms from the accumulation and preservation of dead remaining of plants and animals under the earth crust in a marsh environment. It contains more than 50% of  carbon along with other constituents like hydrogen, oxygen, sulpher etc. 

There are four types of coal on the basis of amount of carbon present in it. They are peat( containing about 50 to 60 percent of carbon), Lignite or Brown coal ( containing 60 - 70 percent of carbon), Sub-Bituminous (containing 70 - 77 percent of carbon), Bituminous ( containing 77 - 89 percent of carbon) and Anthracite or hard coal ( containing 90 - 95 percent of carbon). 
Alternative source of energy:
The cheap and durable source of energy that can be used instead of non-renewable source of energy is called alternative source of energy. Eg: Solar energy, wind energy, tidal energy, biomass etc.

Sun as the ultimate source of energy:

Sun is the main source  of heat and light energy on earth. It radiates about 27×1023 KW energy each second. The average solar energy received by earth every second per 1 sq. meter  is called solar constant and it is estimated to be nearly 1. 4 KWm^-2.  Different types of energy sources in our daily life are the changed forms of solar energy directly or indirectly. Green plants uses sun light to produce food by photosynthesis process. The food produced by plants is consumed by different types of animals to produce energy for their growth and development. Wind blows in the earth's atmosphere due to change in temperature caused by solar energy that helps to run the wind mills and wind turbines. Water cycle maintained by solar energy recharges the under ground water and irrigates the land, runs the electric turbines in hydropower stations. Most of the energy sources that we use today like fossil fuels, bio-fuel, hydroelectricity, tidal energy etc. are dependent upon solar energy directly or indirectly, so, sun is the main source of energy.  

Energy crisis: 
The rate of consumption of the fuel energy is so rapid that they can not last for longer time due to population growth. If the rate of consumption of fuel energy is continuously increases and no other alternative souses of energy are searched, the fuel like petrol, coal diesel, coal, will be finished. This results the world to be in serous problem of energy scarcity. This shortage of energy sources is called energy crisis.

The main causes of energy crisis are:
i. Huge demand of energy sources because of over population.
ii. lack of proper management of non-renewable source of energy.
iii. Over use of non-renewable source of energy.

Ways to solve energy crisis:
i. By using alternative source of energy.
ii. By controlling population growth.
iii. By conserving the existing source of energy.
iv. By proper management of non-renewable source of energy.

Conservation of energy: 
The saving of energy by proper management and utilization to stop the energy crisis is called conservation of energy. Energy can be conserved in the following ways:
i. by using alternative sources of energy.
ii. by promoting the devices which utilize the solar energy, hydro-power, wind energy, tidal energy etc.
iii. by avoiding non-renewable sources of energy as much as possible.

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Pressure

Pressure
Pressure is defined as the force per unit area. It is a scalar quantity. Its SI unit is N/m² or Pascal (Pa). If the force of different magnitude is applied on the same area, the pressure varies. Pressure is  more when more force acts on the body. Likewise, if same force acts on two different areas, the pressure varies. Pressure goes on increasing when force is increased and vice-versa. When force is applied to the small area the pressure and increases when force is applied to a large area.
Let us consider a force 'F' is applied to a certain surface area 'A' , then pressure is directly proportional to the force and inversely proportional to the area of the surface in which the force acts normally. Mathematically,

$P\alpha F$..................(a)

$P\alpha \frac{1}{A}$....................(b)

Combining equation (a) and (b), we get, 

$P\alpha \frac{F}{A}$...............(c)

$P=k\frac{F}{A}$.................(d)

[Where, k is proportionality constant and its value is 1 because when 1 N force is applied in 1 m², the pressure is 1N/m²]

Therefore, 

$P=\frac{F}{A}$....................(e)

Pressure in liquid: 

Let us consider a container with base area 'A' filled with liquid of density 'd'. Let the depth of liquid inside the container be 'h'. 'F' be the force exerted by the liquid on the base of the container which is equal to the weight of the liquid inside the column.

By the definition of pressure,

$P=\frac{F}{A}$..............(a)

$P=\frac{mg}{A}$..............(b) [As, F=mg]

$P=\frac{dvg}{A}$...............(c) [As, d=m/v and m = dv]

$P=\frac{d(A\times h)g}{A}$.........(d) [As, V=A×l]

$P=dgh$.........(e)      

Equation (e) shows that pressure exerted by liquid in a column depends on: 

- density of liquid 'd'

- height of liquid column 'h'

- acceleration due to gravity 'g'

Equation (e) shows that pressure exerted by the liquid is directly proportional to the height of the liquid column, density of the liquid and acceleration due to gravity.

Laws of liquid pressure: 

• Liquid pressure is directly proportional to its density
• liquid pressure at a point is same in all directions within the liquid. 
• Liquid pressure is independent of the shape of the vessel. 
• Liquid pressure is directly proportional to the depth.

Pascal's law:

Pascal's law states that 'Pressure is equally exerted perpendicularly on all directions as pressure is applied at a point on liquid contained in a enclosed container.'
Pascal's law is based on the principle that liquids are in-compressible and liquid transmits pressure equally in all directions. With the help of Pascal's law we can produce large force by applying small forces. In other words Pascal's law amplifies the applied force and helps in doing work. Hydraulic machines were developed on the basis of Pascal's law. Examples of hydraulic machines are hydraulic machine, hydraulic jack and hydraulic lift etc.

Let us consider a F1, F2, F3, and F4 be the forces applied at pistons p1, p2, p3 and p4, at the same time P1,P2, P3 and P4 are the pressures in the respective pistons. According to Pascal's law, pressure at piston p1 is equally distributed in all other pistons. Mathematically,

p1 = p2 = p3 = p4

Similarly, 

$\frac{{{F}_{1}}}{{{A}_{1}}}=\frac{{{F}_{2}}}{{{A}_{2}}}=\frac{{{F}_{3}}}{{{A}_{3}}}=\frac{{{F}_{4}}}{{{A}_{4}}}$

Hydraulic press:

Hydraulic press is a machine that works under the principle of Pascal’s law. It is usually ‘U’ shaped tube filled with liquid and fitted with air tight pistons. It magnifies the applied force. In other words it converts small applied force into large force. When a small force is applied in a piston of small cross-section area, pressure is equally transmitted in all directions; a large force appears over the piston with larger cross-section area.

Hydraulic press

Hydraulic press as a force multiplier:

Let us consider a hydraulic press filled with water and fitted with air pistons P1 and P2 with cross-section area A1 and A2 respectively. Here, area A1 is smaller than area A2.

When force F1 is applied on a small piston in downward direction , it produces force F2 on piston P2 which moves upward direction due to equal transmission of pressure in all direction according to Pascal’s law.

According to Pascal’s law,

Pressure on small cylinder with piston P1 = Pressure on big cylinder with piston P2.

So, P₁ = P₂

Where P₁  and P₂ are pressure on small and big piston.

Or, $\frac{{{F}_{1}}}{{{A}_{1}}}=\frac{{{F}_{2}}}{{{A}_{2}}}$

Or, ${{F}_{2}}=\frac{{{F}_{1}}\times {{A}_{2}}}{{{A}_{1}}}$

Since, A₂ >A₁ then F­₂ >F₁.

Therefore, hydraulic press or hydraulic lift acts as force multiplier. 

Hydraulic brake

A hydraulic brake is a mechanical component used mostly in vehicles which works on Pascals’s law. In consists of a master cylinder filled with a fluid which is attached to the wheel cylinder with the help of a pipe. The wheel cylinder also consists of the same fluid inside it that is connected to the brake shoe. When foot pedal is pressed the piston in master cylinder is pushed inward along with the special fluid. Then the pressure in the master cylinder is transmitted to the wheel cylinder. The pistons in the wheel cylinder apply force to the brake shoe that widens the brake shoe. Widening of break shoe come in contact with the wheel and produces friction. As a result vehicle stops.

Hydraulic brake

Upthrust: 
Thrust is the force acting perpendicular to the surface. Its unit is Newton. Only liquid and gas exerts up-thrust.
We feel easier to lift a bucketful of water until it is under the surface of the water but becomes heavy when it is out of the surface of water. Similarly, we have experienced during swimming it is easier to lift  a friend inside the water but becomes heavy out of the water.  These examples show that when a body is wholly or partially immersed in water, water pushes the body up with certain force. This force is called upthrust.
Upthrust is defined as the upward force exerted by liquid on an object immersed in in the liquid. It is also called buoyant force or bouncy.

How to measure the upthrust:

Let a stone be tied on a string and suspend it with a spring balance, the weight of the stone in the air be w1 N. The weight of the stone will be w2 N when completely immersed inside the water contained in beaker. There is difference between w1 and w2 due the up-thrust exerted by water in upward direction. This difference in weight gives the up-thrust. Mathematically,
Weight of stone air =w1
Weight of stone inside the water = w2
Then,
Up-thrust = Difference in weight in air and water
                = (w1 - w2)N

Archimedes' Principle: 
Archimedes' principle states that when a body is wholly or partially immersed in a liquid, it experiences a loss in wight due to up-thrust which is equal to the weight of the liquid displaced by it.
This principle can be applied for both liquid and gas.

Properties of Archimedes' Principle: 

• This law can be applied for both liquid and gas.
• Archimedes' principle holds true when an object is wholly or partially immersed in liquid. 
• Up-thrust is independent of weight of an object.

Verification of Archimedes' principle: 
Let us tie a stone by a thread with a spring balance. Measure the weight of the stone in the air, let the weight be w1. Insert the stone completely inside the overflow can (Eureka can) filled with water upto the spout. Due to the up-thrust there is loss in weight of the stone, the weight of the stone be w2. At same time place a empty beaker in pan balance just below the spout of overflow can. Consider the weight of the of the beaker be w3. When the stone is inserted into the water it displaces some water which flows out from the spout into the beaker. Let the weight of the displaced water and beaker be w4. Then,

Loss in weight of the stone in water = w1 - w2
Weight of water displaced by water = Weight of beaker and water - weight of the beaker
                                                          = w4 - w3
The loss in weight of the stone w1 - w2 = Weight of water displaced by the stone w4 - w3
                                               Up-thrust  = Weight of liquid displaced

Hence, it found that up-thrust is equal to the weight of water displaced by it.

Density: 
Density is defined as the mass per unit volume. Its is scalar quantity. Its SI unit is kg / m3. Mathematically,
                                             Density $D=\frac{M}{V}$
Relative density: 
Relative density is defined as the ratio of density of a substance to the density of water at 4°C.
Mathematically,
                                             Relative density \[\text{R}\text{.D}=\frac{\text{Density of substance}}{\text{Density of water at 4 }\!\!{}^\circ\!\!\text{ C}}\]
Relative density has no unit because it the ratio between two densities.

Meaning of Relative Density:

• If a substance has relative density less then 1, it will float in the liquid taken.
• If a substance has relative density equal to 1, it will float with completely immersed in the liquid. 
• If a substance has relative density greater then 1, it will sink in the liquid.  

Law of flotation: 
When a body is immersed  in a liquid experiences two types of forces. They are:

        i.The force of gravity directed vertically downward.
        ii.The up thrust directed vertically upward.

Due to the action of these two forces, a body moves in the direction of greater force. There will be three possible cases if an object is immersed in liquid:

1. If the weight of an object is greater than up-thrust, the body will sink to the bottom.
2. If the weight of an object is equal to the up-thrust, the body will remain anywhere inside the liquid.
3. If the weight of an object is less than up-thrust, the body will rise to the surface of the liquid and floats. 

Principle of flotation:
Principle of flotation states that a body floats in liquid if it can displace the liquid equal to its won weight i.e
Weight of floating body = Weight of the liquid displaced = Up-thrust.

When a body is immersed in a liquid, it experiences two type of forces:
       a. Up-thrust: Acting in upward direction.
       b. Gravity: Acting in downward direction.
Due to the action to these two forces, a body will move in the direction of greater force. According to the resultant of the forces, there are three cases:
      i. If the weight of an object is less than up-thrust the body will floats on the surface
         of the liquid in which it is immersed.
      ii. If the weight of an object is equal to the up-thrust, the body can be
          in equilibrium condition at any point in liquid.
      iii. If the weight of an object is greater than up-thrust, the body
           sinks to the bottom
Hydrometer: 

Hydrometer is an instrument used to measure the density of various liquid, based on the principle of flotation. There are two types of hydrometers.They are constant immersion hydrometer and constant weight hydrometer. 
a. Constant weight or variable immersion hydrometer: The hydrometer which measures the density by observing the scale of he floating neck is called constant weight hydrometer. It consists of a bulb containing mercury of lead shots to keep it upright while floating. The stem is unevenly calibrated in kg/m3 or g/cm3 units of density. The numbers denoting density in the stem are bigger at the bottom, decreasing upward because a hydrometer sinks less in liquids having more density and sinks more in liquids of less density. 
b. Constant immersion or variable weight hydrometer: The hydrometer which measure the density by adding the weights to immerse to the constant level is called constant immersion hydrometer. It measures the relative density. It is also called the Nicholson hydrometer. It is made to sink to the same level in the water as well as in the liquid by placing weights on its pan at the top so that it displaces the same volume of liquids.
Atmosphereic pressure: 
The pressure exerted by column of air on unit surface area is called atmospheric pressure. It is measured by barometer. Atmospheric pressure can not be changed by us. The atmospheric pressure at sea level  is considered as normal or slandered pressure. Its value at sea level is about 101300 N per meter or 760 mm of Hg.
Air pressure: 
It is the pressure exerted by the air enclosed in a container. It is measured by manometer. Air pressure inside the enclosed container can be changed.
Barometer:
A barometer is an instrument that is used to measure the atmospheric pressure of certain place. There are two types of barometers, a. Mercury barometer (or  Fortin's barometer )  and   b. Aneroid barometer.
A simple barometer consists of a long glass tube filled with mercury and turned upside down in a container of mercury. It works by balancing the mercury level inside the glass tube against the air pressure outside. The level of mercury in the tube gives the measurement of the air pressure.
Syringe: 
A syringe is a medical instrument which is used to draw blood out from a body and to inject medicine through blood. It consists of three parts; piston, barrel and needle. It is made up of glass or plastic. It has a scale on the barrel that indicates the volume of liquid inside it.
When piston is pulled outward keeping needle inside the medicine or liquid, a partial vacuum is created inside the barrel. As a result, there is low pressure inside it so liquid or medicine flows into the the syringe. Likewise, When the piston is pushed inside, there is high pressure in the barrel and pushes the liquid or medicine out of the syringe.
Air Pump: 
Air pump is an instrument used to pump air inside a tube.
Water Pump:
A water pump is an instrument that is used to pull under-ground water. 

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Force

Force

Force is the external agent which changes or tries to change the state of rest or motion of a body. It is also called pull or push. Its SI unit is Newton (N). It is derived physical quantity. Since it has both magnitude and direction it is a vector quantity.

Force can produce the following effects on a body:

• It can change the direction of motion.
• It can change the speed of a body.
• It can change the state of rest or motion of a body.
• It can change the shape and the size of a body.

Examples of forces are frictional force, gravitational force, magnetic force, centripetal and centrifugal force, nuclear force etc.
The mutual force of attraction between any two heavenly bodies in the universe is called force of gravitation or simply gravitation. Due to this force earth revolve around the sun. Before 1542 AD it was believed that the earth is the center of the solar system and all other plants and sun revolve around the earth which is called geocentric model, proposed by ancient Greek. Later Nicholas Copernicus introduced new model called a heliocentric model in which sun is the center of the solar system and earth revolve around the sun including remaining plants.

Consequences of gravitational force:

• Existence of atmosphere
• Existence of solar system.
• Revolution of satellites around the planets.
• Revolution of artificial satellites around the earth
• Revolution of planets around the planets.

Newton’s Universal law of gravitation:

Newton’s law of gravitation states that “The force of gravitation between two masses or bodies anywhere in the universe is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers”.

It is called universal law because this law holds true for all the bodies, whether it is massive or microscopic placed anywhere in the universe. The effect of gravitation is more in liquid than in solid because inter-molecular force of attraction is less in liquid and it is weaker than in solid.

Consider, two bodes with mass m₁ and m₂ which are 'd' distance apart from their centers.

According to Newton’s law of gravitation,

$F\alpha {{m}_{1}}{{m}_{2}}$..............................1

$F\alpha \frac{1}{{{d}^{2}}}$...............................2

Combining equation 1 and 2 we get,

Or, $F\alpha \frac{{{m}_{1}}{{m}_{2}}}{{{d}^{2}}}$.....................3

Therefore, $F= \frac{G{{m}_{1}}{{m}_{2}}}{{{d}^{2}}}$......................................4

Where, G is a proportionality constant which is commonly known as universal gravitational constant and its value is 6.67×10 -11 Nm²kg ^{– 2} .

From equation (4) it is found that there exists a force of attraction between any two bodies in the universe separated by some distance. The force acting between the bodies has the following features:

• This force is attractive in nature
• The direction of force is along the line joining their centers.

Definition of G:

According to Newton’s law of gravitation,

$F=\ \frac{G{{m}_{1}}{{m}_{2}}}{{{d}^{2}}}$

If we put the value of m₁ =1kg and m₂ = 2 kg and d = 1m in above expression, we get

F = G ……………………5

From equation (iv) we can define gravitational constant as ‘The force of attraction between two bodies, each with a mass of 1kg kept at a distance of 1 meter apart.

Value of G = 6.67×10 -11 Nm²kg ^{– 2} was found experimentally by Henry Cavendish. This value of G shows that gravitational force is very weak force. The value of G is independent of the nature and composition of masses and medium in which they remain. It cannot be noticed if the two masses are small but becomes noticeable when the two bodies are extremely large.

G is called a universal gravitational constant because it exist everywhere in the universe and it is applicable to all the objects in the universe whether the objects are terrestrial or celestial or of space.

Gravity:
Gravity of a planet or satellite is defined as 'The gravitational force between a planet or satellite and a body on or near to ifs surface.' It is always directed towards the centere of the object. Due to gravity an object acquires weight. 

Let us consider the mass of earth be 'M' and an object is place on the surface of  the earth. The distance between their centers be 'R' which is nearly equal to the radius of the earth.

According to Newton's law of gravitation;

 $F=\ \frac{G{{m}_{1}}{{m}_{2}}}{{{R}^{2}}}$  .........i

or, $mg=\frac{GMm}{{{R}^{2}}}$                      [$\because $F=W=mg]

Where, 
            M=mass of earth
            R=Radius of earth
            W=Weight of the object
            G=Gravitational constant= 6.67×10 -11 Nm²kg ^{– 2}

or, $g=\frac{GM}{{{R}^{2}}}$

or, $g\alpha \frac{GM}{{{R}^{2}}}$...................ii

Here, equation (ii) shows that gravity of a planet is directly proportional to the Mass of the planet or satellite (M) that means if the radius of the planet is increased keeping mass M constant, the gravity will be less and if the radius is decreased, the gravity will increase. 
Equation (ii) also shows that acceleration due to gravity is independent of mass of and object.

Differences between gravity and gravitation:

Sn	Gravity	Gravitation
1	Gravity is the force between a planet or a satellite and a body on or near to the surface	Gravitation is the mutual force of attraction between two heavenly bodies in the universe
2	It is not universal force.	It is universal force.
3	It is expressed as $F=\frac{GMm}{{{R}^{2}}}$	It is expressed as $F=\frac{G{{M}_{1}}{{M}_{2}}}{{{d}^{2}}}$
4	Due to gravity all the objects fall towards the earth or planet.	Due to gravitation, the earth and other planets revolve around the sun.

Acceleration due to gravity: 

Before the Galileo's idea of falling bodies, Greek philosopher, Aristotle believed that when heavy body and light body fall form the same height, the heavier one falls faster on the earth than the lighter one which which was prove to be wrong after Galileo's experiment. According to Galileo the heavier and the lighter objects fall simultaneously on the earth surface. In other words, the acceleration produced on freely falling objects does not depend on the mass.
When Galileo performed the experiment with feather and coin, he found that feather fall more slowly than the coin. It was found that feather fell slowly due to the air resistance when Newton performed the experiment in both in vacuum and air. In vacuum where there is no air resistance both the coin and feather fell simultaneously.

Feather and coin experiment in air

Every object thrown upward falls towards the center of the earth with increase in velocity and hits the ground. The increase in the velocity of an object with produces acceleration on it. The acceleration produced on a freely falling body due to the force of gravity is called acceleration due to gravity. It is denoted by 'g' and its unit is m/s².

Feather and coin experiment in vacuum

Variation of acceleration due to gravity: 
i. Variation of acceleration due to gravity due to the shape of earth:
Earth is not perfectly spherical in shape. It is bulged out in the equatorial region and flattened in the polar regions. So, the radius towards the pole is smaller than the radius towards the equatorial region i.e R_e>R_p. Hence the value of acceleration due to gravity varies from place to place on earth. The value of acceleration due to gravity is 9.78 m/s² at equator and 9.83 m/s² at poles.

ii. Variation of acceleration due to gravity with altitude: 
If we consider the radius of the earth be 'R' at the surface 'h' be the distance at certain height above the surface of the earth. Then the total distance between the center of the earth and the point at certain height 'h' be (R+h). Then,

Acceleration at surface of the earth is $g=\frac{GM}{{{R}^{2}}}$  ........................a

Acceleration at certain height 'h' is ${{g}^{'}}=\frac{GM}{{{(R+h)}^{2}}}$......................b
Putting the value of GM=gR2 from equation (a) in equation (b) we get,

$g={{g}^{'}}\frac{{{R}^{2}}}{{{(R+h)}^{2}}}$

iii) Variation of acceleration due to gravity with depth: 

If we consider the earth to be a perfect sphere of mass M and radius R. Let 'P' be any point 'x' under the surface of the earth.Then acceleration due to gravity at point 'p' will be,

$g=\frac{GM}{{{(R-x)}^{2}}}$

Here, R-x is less than R, so the value of 'g' under the surface is less than at the surface.

Differences between Acceleration due to gravity (g) and Gravitational constant (G):

S.no	Acceleration due to gravity (g)	Gravitational constant (G)
1	It is acceleration produced on a freely falling body due to gravity.	It is the mutual force of attraction between two bodies with unit mass kept at 1m distance.
2	It is vector quantity.	It is scalar quantity.
3	It differs from place to place.	It remains constant everywhere.
4	It unit is m/s2	Its unit is Nm2/Kg2.

Differences between Acceleration due to gravity and gravity: 

S.no	Acceleration due to gravity (g)	Gravity
1	It is acceleration produced on a freely falling body due to gravity.	It is the force of attraction between planet or satellite and an object on or near to the surface.
2	It is the effect of gravity.	It is the cause of the acceleration due to gravity.
3	It unit is m/s2	Its unit is N.

Free fall:
 The falling of an object towards the center of another object without any external resistance is called free fall. In other words, the falling of an object with an acceleration equal to the acceleration produced by the pull of the earth is called free fall. E.g. The falling of an object on the surface of the moon.
Weightlessness: 
The condition in which the weight of an object seems to be zero is called weightlessness. It is also called as the apparent loss of weight of an object. The state of weightlessness can be observed in the following conditions:

• A body at the centere of the earth.
• A body in a freely falling elevator or lift.
• A body in the neutral point in space.
• A body inside the satellite orbiting a planet. 

Differences between free fall and weightlessness:

S.no	Free fall	Weightlessness
1	The motion possessed by a body without any external resistance is called free fall.	The condition in which the weight of an object seems to be zero.
2	It is cause of weightlessness.	It is the effect of free fall.

Differences between Weightlessness during free fall and Weightlessness in space: 

S.no	Weightlessness in free fall	Weightlessness in space
1	It occurs during free fall of an object.	It occurs when acceleration due to gravity is zero.
2	In this condition, a = g.	In this condition, g = 0.
3	It occurs due to gravity	It does not occur under the influence of gravity.
4	It occurs within the gravitational field.	It occurs in the outer space.
5	It is apparent weightlessness	It is true weightlessness.

Mass: The quantity of matter contained in a body is called mass of that object. Its SI unit is 'Kg'. It  is scalar quantity and measured by beam balance. It is a constant quantity. It can be zero.

Weight: It is the measurement of force of gravity acts on a body. It is a vector quantity with SI unit 'N'. It is measured by spring balance. Weight of an object will be zero, at the centere of the earth or at the place where R = 0.  
Differences between Mass and Weight: 

S.no	Mass	Weight
1	It is the quantity of matter contained in a body.	It is the amount of force of gravity acted on a body.
2	Mass of an object does not vary from place to place	Weight of an object varies from place to place.
3	Mass is scalar quantity	Wight is the vector quantity.
4	Mass is measured by beam balance.	It is measured by spring balance.
5	There is no place or condition under which mass of an object be zero.	Weight of an object will be zero, at the centere of the earth or at the place where R = 0.
6	The SI unit of mass is kilogram(Kg).	The SI unit of weight is Newton(N).

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