Gravitation [ in English ]

 Gravitation

Gravitation

Newton's law of gravitation :-

Every body in this universe attracts every other body with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between there centres. 

i e

Or

The constant G is called the universal gravitational constant

In S I  units the value of G is

In Vector form

Vector dirrected along AB

i e

dirrected along the line joining their centres

Or

Vector Form 

which is Newtons 3rd law of motion

=) gravitational force of attraction between two particles are equal in magnitude  but, opposite 

in sign

The centres of two masse

 So gravitational force is a central force.

Dimensional formula for G

Note the value of G does not depend upon the nature and size of the bodies.

* It does not depend upon The nature of medium between the two bodies.

Properties of gravitational Force

(1) gravitational force is always attractive

medium between two masses.

 (a) It is a central force i e  it acts along the line joining the centres of two bodies.

(4) It is the weakest force in nature 

(5) It is a conservative force I. e work done by it is path independent.

Gravity

The force of attraction exerted by the Earth on The body is called gravity or gravitational pul.l The acceleration produced in the motion of a body by the gravitational force of Earth is called acc. due to gravity and is denoted by g. The Value of g. by g on or hear the surface of earth is 9.8m/s². It is always directed vertically down towards the centre of the earth. 

Relation between g and -G

If the body of mass m lies The surface of the earth  or near its surface

Then

where M = mass of the Earth

          R = radius of the Earth

From this it follows that

g does not depend upon the mass m of a body.

Hence all bodies will fall on the earth  with same acceleration.

i.e all objects hollow or solid, big or small will strike the ground at the same time.

As g = (G / M) / R²

= G . (volume × density) / R²

= G   (4/3) * π  R³ * ρ / R²

= (4 /3 π GR ρ * R) / 3

Note: Mass of the Earth is 

M = 10²⁴ kg

and radius is

R = 6400 km

As we know density ρ = mass / volume

=> mass = volume × density

=> M = V * ρ

Variation of g

-------------------------

The value of g varies due

The value

to

(1) height (altitude)

2)Depth below the surface of south

(3) Shape of the Earth

(4) Rotation of the earth.

 

(1) the value of g at a height h above the surface of Earth

gh = GM/(R+h)२

where R= radius of Earth

If the body lies on the surface of the

Earth Then h=0

gh= GM/R२=g

Also gh= g ( 1-2h/R), h  R

(2) The value of g at the depth d below the surface of Earth is

gd = (1- d/R)

R

at the contre of the earth 

d=R

gd =0

Note the value of g is maximum on The surface of Earth it decreases with height and also with depth

(3) As we move from the equator towards the poles the value of g increases because Polar radius is less than equitorial radius.

g pole > g equates.

the weight of the body increases as it is taken from equator to the poles.

key points:-

em

(1)

g = GM/R२

(2)  gh = GM/(R+h)२

(3)  gh = g ( 1-2h/R)

(4) = gd= g ( 1- d/r)

At the centre of the Earth

 g = 0

Question 

If the distance between masses is doubled, the gravitational attraction between them

(a) is doubled 

(b) is reduced to quarter

Sol.

F = Gm1m२/r२