## Gravitation

Gravitation is the chapter of Physics covers the syllabus of class 9 th that covers Newton’s Gravitation law, acceleration due to gravity, freely fall body, Thrust and Principle of Archimedes.

GRAVITATION FORCE OF EARTH :

If we release a small stone without pushing it from a height it accelerated towards the earth. the stone is when accelerated towards the earth it means that some force is acting on it .

The force which pulls the objects towards the Centre of the earth is known as gravitational force of the earth.

The stone also attracts the earth, it means every object in the universe attracts every other objects

NEWTON’S UNIERVERSAL LAW OF GRAVITATION :

Sir Isaac Newton in 1687 proposed a law about the force of attraction between the two objects in the universe which is called Newton’s law of gravitation.

It states that Every mass in this universe attracts every other mass with a force which is directly proportional to the product of the mass and inversely proportional to the square of to distance between them.

let mass m1 and m2 distance r than force of attraction F

F∝ m1xm2 ___________1

F∝ 1/r²———–2

combing the equation 1 &2

F=G m1xm2/ r²

G is the gravitational Constant = 6.67 x10 ¯¹¹ N m¯²/ kg²

RELATION BETWEEN IIIrd law of motion and Newton’s law of gravitation :

According to Newton’s 3rd law of motion that Every object exerts equal and opposite force on the other object but opposite direction and in Newton’s law of gravitation that every mass in the universe attracts every other mass.

Incase of freely falling stone and earth, stone is attracted towards the earth means the earth attracts the stone but according to Newton’s third law of motion,

the stone should also attract the earth really it is true that stone also attracts the earth with the same force

F= ma F=m1xm2/r²

so g towards the earth = 9.8 m/s² but acceleration towards the stone is very less

IMPORTANCE OF UNIVERSAL LAW OF GRAVITATION :

It is the force that binds us to the earth , the motion of moon around the earth , the motion of the earth around the sun , The tides due to moon in the sea .

This fall under the influence of the earth is called ‘ free fall of an object ”

During this free fall direction do not change but the velocity continuously changes which is called acceleration due to gravity denoted by g unit m/s^2

GRAVTATIONAL ACCELERATION AND IT’S VALUE AT THE SURFACE OF THE EARTH :

The uniform acceleration produced in a freely falling body due to the gravitational force of the earth, is called acceleration due to gravity. It is denoted by “g” it always acts towards the Centre of the earth

Let us suppose mass of earth M , mass of body placed on the earth be m than the force of attraction on the surface of earth if radius of earth be R

F= GMm/R² which is equal to weight of body = mg

mg= GMm/R²

=> g= GM/R²

DIFFERENCE BETWEEN MASS AND WEIGHT :

We can measure mass of object by the inertia, the total quantity of matter contained in the body is called mass of the body, it always remain constant and measured by beam balance .

whereas weight is equal to product of mass and acceleration due to gravity It is the gravitational force by which earth attracts an objects , it depends upon g so it vary with the value of g itis measured by spring balance

VARIATION IN THE VALUE OF” g’ Earth is not perfectly spherical .

The radius of earth at equator is more than the radius of earth at poles so value of “g” is mimimum at equator and maximum at pole

Examples :

If the height of an object from the Centre of the earth is made double than value of g becomes 1/4 times of g at earth The value of g decreases as either go up / high from the surface of earth or we go inside the earth.

Weight of the object on the surface of moon is 1/6 of the surface on the earth because value of g on moon is 1/6 times of the value of g at earth. suppose a person weighs 600 newton on earth he will weigh 100 newton at moon .

THRUST

It is the force acting on the object perpendicular to the surface of the object.

PRESSURE :

Thrust per unit aera is called pressure

Pressure = Force/ aera

Newton /meter² or Pascal (unit )

FACTORS ON WHICH PRESSURE DEPENDS :

a) Applied Force

b) Aera of surface on which force acts .

Examples

a) The base of high buildings is made wider so that weight of walls act over a large surface aera and reduce the pressure

b) School bags are having broad strap so that the weight of school bags fall over the large surface aera of the shoulder which reduces the pressure of the bags over shoulder

c) The blades of knives are sharp as the surface aera is less so less force is applied to cut vegetables/ fruits

d) All liquids or gases are fluid which exert pressure in all direction over the walls of containers.

BUOYANCY

It is the upward force experienced by an object when it is immersed wholly/partially into the liquid/ fluid It acts in upward direction and depends on the density of the fluid volume of object immersed in fluid

LAWS OF FLOTATION

a)When the force of gravitation attraction of the earth on the surface of the object/ weight of the object < or = to the buoyant force exerted by the fluid on the surface of object than the object always floats.

b) When the force of gravitation attraction of earth on the surface of the object is more than the buoyant force exerted by the fluid on the surface of object than the body sinks in liquid that is why ship floats on the surface of water but small pin sinks

DENSITY :

The mass per unit volume is called density of the body

If Mis the mass Vis the volume d is the density than d= M/V

SI unit kg/ meter³

ARCHIMEDES PRINCIPLE :

When a body is immersed wholly or partially in the liquid it experiences apparent a loss of weight which equal to the weight to the liquid displaced my the immersed body.

This principle is mostly used in determining the relative density of substances, it is also used in designing the ships/ submarine , the lactometer/ hydrometer works on this principle.

RELATIVE DENSITY :

It is the ratio of density of substance to the density of water at 4Deg C

RD = Density of substance/ density of water It has no unit because of being ratio

Volume of substance x density = Volume of immersed part of body x density of liquid

Examples :

a) Relative density of gold is 19.3 density of water is 1000 kg/m^3 than density of gold is by definition RD = Density of substance/ density of water

19.3 = density of gold/ density of water

density of gold = 19.3x 1000=19300 kg/m³

Example

b) Volume of 0.025m^3 of aluminum mass id 67kg than the density is mass/ volume

67/0.025 =2680 kg/m³.

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Read More: Force and laws of Motion