This document discusses the universal law of gravitation and its implications. It can be summarized as follows: 1) The universal law of gravitation states that the gravitational force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. 2) This law explains phenomena like the orbit of planets around the sun and the moon around Earth. It also explains why objects fall with an acceleration of 9.8 m/s^2 on Earth. 3) The weight of an object, which is the gravitational force exerted by Earth, differs on other celestial bodies due to differences in their masses and radii. Calculations show an object's weight on

1. Gravitation
All objects in the universe attract
each other. This force of attraction
between objects is called gravitational
force.

7. Universal law of Gravitation
According to universal law of gravitation, the force
between two Objects is directly proportional to the
product of their masses.
F ∞ M X m
And the force between the two objects is inversely
proportional to the square of the distance.
F ∞ 1/d2
Combining above two Eqs…
F ∞ M X m /d2

8. Universal law of Gravitation
G  Universal Gravitational Constant
( G=6.67X 10-11 N m2 kg-2 )
m1,m2  unknown masses
d2 `  Square of the distance

9. Importance of the Universal Law of Gravitation
* The force that binds us to the earth
* The motion of the moon around the earth
* The motion of planets around the sun
* The tides due to the moon and the sun.

10. Free Fall
F = G M m / d2
F = m g
m g = G M m / d2
g = G M / d2
‘d’ replaced by ‘R’
R  Radius of the earth (R= 6.4X106 m)
g = G M / R2

11. To Calculate the Value of g :
G= 6.7 X 10-11 N m2 kg-2
M= 6X1024 kg
R= 6.4X106 m
g = G M / R2
= 6.7 X 10-11 N m2 kg-2 X 6X1024 kg / (6.4X106)2 m
g = 9.8 m s-2

12. Motion of Objects under the influence of
Gravitational Force of the earth :
As g is Constant near the earth, all the equations for
the uniformly accelerated motion of objects become valid
with acceleration a replaced g.
The equation of Motion are:
v= u + at
s= ut+1/2 at2
v2= u2+2as
Where u , v are the Initial & Final Velocities and s
is the distance covered in time t.

13. Mass
The mass of an object is the measure of its inertia.
The greater the mass, the greater is the inertia. It remains
the same whether the object is on the earth, the moon or
even in outer space. Thus, the mass of an object is constant
and does not change from Place to Place.
Weight
The earth attracts every object with a certain force
and this force depends on the mass(m) of the object and the
acceleration due to the gravity(g).

14. Weight
The weight of an object is the force with
which it is attracted towards the earth.
W.K.T F = ma  F = mg
The Force of attraction of the earth on an object is
known as the weight of the object.
W = mg
As the weight of an object is the force with which
it is attracted towards the earth.

15. Weight of the object on the Moon
Earth
Mass M = 5.98X1024 kg
Radius R = 6.37X106 m
Moon
Mass m = 7.36X1022 kg
Radius R = 1.74 X 106 m

16. Wm = G Mm X m / Rm
2
Wm = G 7.36X1022 kg X m / (1.74X106 m)2
Wm = 2.431X 1010 G X m
Similarly,
We = G Me X m / R2
e
We = 1.474X1011 G X m
Wm/We = 0.165 ≈ 1/6

17. Weight of the object on the moon / Weight
of the object on the earth = 1/6
Weight of the object of the moon=1/6 X
Weight of the object on the earth

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