JEE board exam Gravitation important notes and important topics discuss

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I ntroduction :

There are 4 types of forces in nature :
(i) Gravitational force
(ii) The electromagnetic force
(iii) The strong nuclear force (also called hadronic forces)
(iv) The weak nuclear force
Gravitational force is the weakest force among the four fundamental forces of nature.
Although of being negligible importance in the interaction of large objects. It is gravity that holds
the universe together.
In this chapter we will learn basic laws that govern gravitational interaction.

Newton’s Laws of Gravitation

In 1687 Newton published the law of gravitation.
It states that „every particle in the universe attracts every other particle with a force directly
proportional to the product of their masses and inversely proportional to the square of the distance
between them.‰
Consider two bodies A and B of masses m1 and m2. Let r be the distance between the centres and
F be the force of attraction between them.


 
F12 F21


A r B



According to NewtonÊs law of gravitation

m1 m2
F
r2

Gm1m2
F
r2

In vector notation

  Gm1 m2
F12  2
r→12
r12



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Characterstics of gravitational force :
(i) It is conservative in nature
(ii) It is a central force
(iii) It is independent of the medium between the particles

Example 1

Sphere of mass 60 kg is attracted by second sphere of mass 40 kg with a force 4 mgf.
Calculate distance between them.
Given that m 1 = 60 kg, m 2 = 40 kg G = 6 1011 Nm2 kg 2

6
Solution : F = 4mgf = 4 10 10
5
= 4 10 N

Gm1 m2
F=
r2


G m1 m2 6  10 11  40  60
r 
F 4  105

r = .06 m = 6 cm

Acceleration due to Gravity

Gravity : If one of the bodies in expression of NewtonÊs law of gravitation is earth than the
gravitation is called gravity. Hence gravity is force by which earth attracts a body towards its
centre.
When a body is dropped from a certain height above the ground it begins to fall towards the earth
under gravity. The acceleration produced in the body due to gravity is called the acceleration due
to gravity. It is denoted by g. Its value close to the earthÊs surface is 9.8 m/s2.
Suppose that the mass of the earth is M, its radius is R, then the force of attraction acting on a
body of mass m close to the surface of earth is

GMm
F=
R2
According to NewtonÊs second law, the acceleration due to gravity

F GM
g 
m R2

In vector form,

 GM →
g 2 R
R
 
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
where R is position vector from earthÊs centre to the body of mass m.

Body of mass m


R




Earth of mass m

This expression is free from m. If two bodies of different masses are allowed to fall freely they will
have the same acceleration, i.e., if they are allowed to fall from the same height, they will reach
the earth simultaneously.

Variation of acceleration due to gravity

The value of acceleration due to gravity changes with height (i.e., altitude), depth, shape of the
earth and rotation of earth about its own axis. The effect of each of the above factors on the value
of g has been discussion below.
(a) Effect of Altitude : Consider earth to be a sphere of mass M, radius R with centre at O.
Let g be the value of acceleration due to gravity at a point A on the surface of earth.

B g´
h
A g

R

O



GM
 g= ...(1)
R2

If g´ is the acceleration due to gravity at a point B, at a height h above the surface of earth,
then

GM
g´ 
...(2)
 R + h 2


GRAVITATION