Law of gravitation|Class 9|Class 11

Gravitation

  Each and every object in the universe attract each other. This phenomena is called gravitation.

For example:-

(1)    Apple falls to the ground.

(2)   Planets moves around the sun.

(3)   Galaxies are also caused by the gravitation.

Universal Law of gravitation

Every object in the universe attract each other with a force which is proportional to the product of their mass and inversely proportional to the square of the distance between them.

       F=GM₁×m₂/R2

where F=Gravitational constant

           M₁=Mass of 1st object

          M₂= Mass of 2nd object

           R²=Square of distance

           G=Gravitational constant

Proves of gravitational constant

Let the object be A and B of masses M and m lie at the distance of r.

 

According to the Law of gravitation:-

   F α M₁×m₂--------------- (1)

   F α 1/r²-------------------- (2)

Combining equation (1) and (2)

 We get,

F α M₁×m₂/r²

G is constant

F = G×M₁×m₂    Proved

SI unit of G =Nm²/kg²

Value of G = 6.67×10^-11

Importance of the universal Law of gravitation.

●       The force that connected to the earth.

●       The motion of the moon around the earth.

●       The planets move around the sun.

●       The tides due to the moon and the sun.

Kepler's Law

The three Kepler's law states as follows:-

(1) Law of orbits:- Every planets move around the sun in an elliptical orbits and the the sun is located one of the foci.

(2) Law of areas:-Every planet sweeps out equal areas in equal interval of time.

   This law comes from the observation of the planets appear to be slower when they are farther from the sun than when r they are nearer to the sun they move faster.

(3) Law of periods:- The square of time period of the revolution of the earth is directly proportional cube of distance. 

                       T² α R³

Why law of period true?

We know that,

F=G×M×m/r2

Fe=mv2/r

So,

⇒Mv²/r=GMm/r²

⇒v² =Gm

⇒(2πr/t)²=GM/R

⇒ 4π²r²/t²=Gm/R

By cross multiplying

=4π²r3=Gmt²

  = r³α t³  (because 4π2, G, M are constant)

     r³αt³ Proved

Newton Inverse square rule

Let the orbital velocity is v and the radius of the orbit is r.

We know that,

FαV2/r ------------------------------(1)

If t denotes the period 

v=2πr/T

So that v2αr2/t2

We can write as

v2 α r2/t2

We can write as

v2α(1/r)x(r3/t2)

Since r3/t2 is constant by kepler’s third law 

We have,

v2α1/r------------------------------(2)

Combining equation (1) and (2),

We get

F α v2/r

We can write as,

F α1/r2

 It means that if the distance will increase the force will decrease.

Free fall

When the object falls towards the earth the acceleration due to the gravity acts upon it not the acceleration of the object.

Free fall depends only on  acceleration due to the gravity, not on the mass of the object.

Calculation of the value of g 

We know that,

F=GxMxm/r2

mg=GxMxm/r2

g=GxM/r2 

(Mass of the earth=6x10-24

Radius of the earth=6.4x106)

g=6.67x10-11x6x1024/(6.4x106m)2

g=9.8 ms-2  

ESCAPE SPEED

Escape speed is the minimum speed required to allow an object to escape from the gravitational influence of the earth to go into space.

       The escape speed in the earth is 11.2 km/s.

MASS

The amount of matter present in the  substance is known as the mass.Mass is the constant term which means the mass does not change.

WEIGHT

The weight of the object is the force with which it is attracted towards the earth.

We know that,

F=mxa

That is,

F=mxg(g=acceleration due to the gravity)

So we can write as

W=mxg

(W=weight

m=mass

g=acceleration due to the gravity).

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