**INTRODUCTION**

In a cricket match when batsman hit the ball with his bat, ball will go upward and after sometime it comes back on the ground . In chapter of motion we learnt about the force is the cause of motion but when ball reaches its top position why it comes back on the ground …?

This is due to gravitation .Any object falling towards earth , Moon goes around the earth ,fixation of atmoshphere on earth, any artificial or natural satellite moving around its planet . sir Isaac newton found that same force is responsible for all these, and this force is called GRAVITATIONAL FORCE

__WHAT IS GRAVITATIONAL FORCE…..?__

Any body which has mass attracts another body of mass i.e *force of attraction between two masses is called gravitational force.*

**The universal law of gravitation (**Newton’s law of Gravitation**):**

*Every object in the universe attracts every other object with a force which is proportional to the product of their masses and inversely proportional to the square of the distance between them*.

Let two objects A and B of masses M and m lie at a distance of **d** from each other as shown in the figure.

Let F be the force of attraction between the objects A and B

According to the statement of universal law of gravitation

** F **α** **** Mm **…….1

And

**F** α** 1/d ^{2} **…….2

So combining both 1 and 2

** F** α** Mm/d ^{2} **……..3

After eliminating proportional sign we put **G **as a constant

i.e

**F=G Mm/d ^{2}** ……….4

G is called a universal constant because its value does not depend on the nature of intervening medium or temperature or any other physical variable.

**G= Fd ^{2}/Mm **……….5

Equation 5 is equation of universal law of gravitation

S.I. unit of **G = Nm ^{2}/kg^{-2 } **

Value of

**G = 6.673 x 10**(Found by Henry Cavendish)

^{-11 }Nm^{2}/kg^{-2}If we want to define gravitational constant, then, we have to take all values as unity except G and F i.e

Consider two bodies of masses 1 kg each separated by distance 1 m, then the expression becomes:

**G=F(1 meter ) ^{2} / 1 kg x 1kg **……………..6

** G=F **……..7

So, from eq 6 and eq 7 we can define G as:*Gravitational constant is equal to the force of attraction that exists between two bodies of unit masses separated by distance one meter**.*

__APPLICATION OF THE UNIVERSAL LAW OF GRAVITATION__

- This force holds the buildings and objects to the earth
- The motion of planets around the sun
- Sea tides due to gravitation of the moon and the sun
- It keeps water retained in oceans
- It holds the atmosphere in place

**FREE FALL**

** **Suppose you are standing on a multistory building and drop a tennis ball from the top ,just a moment after releasing the ball it starts falling downward and from that time only gravitational force is acting on it. This type of body is called freely falling body . i.e The bodies that fall under the influence of gravity alone are called freely falling bodies.

**ACCELERATION DUE TO GRAVITY**

From the above example when the ball is coming downward or starts motion, the magnitude of the velocity changes due to earth’s attraction and any change in velocity involves acceleration .This acceleration is produced in the ball only by the effect of gravitational force ,this acceleration is called * acceleration due to gravity* . it is the acceleration produced in the freely falling bodies due to earth’s gravity

This acceleration or (acceleration due to gravity) is denoted by ‘**g**’ , it has the same unit as that of acceleration i.e **‘ms ^{-2}’.**

**TO CALCULATE THE VALUE OF ‘g’**

Let us consider a object placed on earth with mass ‘m’ , mass of earth is ‘M’ and distance between earth’s centre to centre of object is ‘d’

If the object is placed on earth surface and earth attracts it with a force than the force produced in the object must be multiplication of mass of object and acceleration produced in it (according to Newton’s second law of motion)

i.e

** F=ma **………8

** **but here the acceleration is acceleration due to gravity i.e ‘g’

so eq^{n } 8 becomes

**F=mg **………9

Now according to universal law of gravitation i.e eq^{n} 4

** F=G Mm/d ^{2} **

Putting the eq^{n } 9 in above equation

We get

**mg** =** G Mm/d ^{2} **……..10

or **g=GM/d ^{2}** …….11

since the object is palced on earth the distance between both is nearly equal to radius of the earth because in compare to earth radius object is negligible so we consider the distance as equal to radius of earth.

i.e d —> R

so eq^{n} 11 becomes

**g=GM/R ^{2}** ……………..12

Now to calculate the value of ‘g’ we should put the value of G,M,and R in eq^{n }12

G (universal gravitational constant) = 6.7 x 10^{-11} Nm^{2}/kg^{-2} ,

M (mass of earth) = 6×10^{24 } kg ,

R (radius of earth) =6.4×10^{6} m

By putting these eq^{n} 12 becomes

this is the value of acceleration due to gravity.

the value of g is different on different planets as mass and radius is different for all.

**Motion of different object in influence of gravitational force:- **In the eq^{n} 13 the value of ‘g’ does not depend on mass of object it only depend on mass of earth so we can consider that the acceleration produced in the every object is independent of its own mass and have same rate .

So we can say that the value of g is constant near the earth .According to the newton’s law of motion the value of ‘a’ can be replaced by ‘g’

then equation becomes

**NOTE:- **While applying the eq^{n} 14 , ‘g’ is positive when it is in direction of motion i.e falling from a hight ,and ‘g’ is taken as negative when it is in opposite direction of motion i.e going upward .When the body is dropped from a height, Initial velocity (u) = 0, When the body is thrown upwards, then final velocity (v) = 0

**MASS:- **

** **when we go to market and but potato from vegetable vendor we ask for one kg potato ,here we ask for the amount of matter present in patoto, this is known as mass .i.e

*mass is measure of the amount of matter present in the object .*

Mass is denoted by ‘M’ and SI unit of mass is ‘Kg’ since it has only magnitude it is a scalar quantity. Mass does not depend upon gravity and is constant everywhere and never can be zero .

**Weight:-**

It is the pull exerted on a body by earth or a force with which the earth attracts objects towards itself or *it is the measure of amount of force exerted on a mass of body due to acceleration due to gravity* . It is a vector quantity and is measured in Newtons and denoted by W. Weight is different at different places as it depends upon ‘g’ and it is different at different places or planets.

**DIFFERENCE BETWEEN MASS AND WEIGHT**

MASS | WEIGHT |

Mass is simply the measure of the amount of matter in a body. | Weight is the measure of the amount of force acting on a mass due to acceleration due to gravity. |

Mass is denoted by “M” | Weight is denoted by “W”. |

Mass is always constant for a body and there are several formulas to calculate mass.One way to calculate mass is: Mass = volume × density M=V x d | Weight is the measure of the gravitational force acting on a body.Weight can be calculated from the following formula: Weight = mass × acceleration due to Gravity W= M x g |

Mass does not depend upon gravity and is constant everywhere. Mass can never be zero. | Weight is dependent on the gravity and so, it varies from place to place. Weight can be zero where there is no gravity (like space). |

The SI unit of mass is Kilogram (Kg). | The SI unit of weight is Newton (N). |

**Weight of object on Moon and Earth**

Dividing eq^{n }15 by eq^{n} 13 i.e

Moon(g)/ Earth(g) = 1.6 ms^{2} /9.8 ms^{2} =1/6 ………..16

From eq^{n} 16 we see that the weight of object on Earth is becomes 1/6 on Moon.

**THRUST:-**

** **Here we have three picture and there is a force applying on it ,but in picture II we see that the force is applying perpendicular that is 90^{o} to its surface . This force is called thrust

*THRUST is the force acting on an object perpendicular to its surface *The effect of thrust depend on the area on which it acts.

The unit of thrust is that of same as force i.e **N **.

**PRESSURE:- ***The force acting perpendicular on unit area of surface is called pressure.*

SI unit:- force per unit area i.e *Nm ^{-2}*

From the formula of pressure it is clear that same force can produce different pressure depending on area which it acts.

**Fluids :- **All liquids and gases are together called **fluids **. As similar as solid that exert pressure on any surface fluids also exert pressure because it also have weight . fluids exert pressure on wall surface of container it kept. And it exert pressure in all directions.

**Buoyancy:-**The tendency of a liquid to exert an upwad force on an object immersed in it is **buoyancy** .

**BUOYANT FORCE:-** the upward force which acts on object is called **buoyant force**. Also called as **Upthrust.**

**DENSITY:- **The density of substance is defined as mass per unit volume

SI unit of density –> kg per meter cube (kgm^{-3})

** ARCHIMEDES PRINCIPLE :- **

**Statement —**(*When an object is fully or partially immersed in a liquid ,it experiences a buoyant force ,which is equal to the weight of liquid displaced by the object*)

i.e According to the principle “ an object will float in a liquid ,if the weight of object is equal to the weight of liquid displaced by it. This is also called of floatation.

*Buoyant force acting on an object= Weight of liquid displaced by the object*

**APPLICATION OF ARCHIMEDES’ PRINCIPLE:-**

- It is used in determining relative density of substances.
- Hydrometers used to determine the density of liquids, work on this principle.
- Lactometers used to determine purity of milk, are also based on this principle.

**RELATIVE DENSITY****:-**

** ***The relative density of a substance is the ratio of its density to the density of water .*

Since the relative density is ratio of similar quantity so it has no unit.

The relative density of a substance is found accurately by using Archimedes principle.

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