Detailed notes on the topic Gravitation

1. Gravitation
Hello Friends
Let us first understand as to what do we mean by the word Gravitation.
What is Gravitation?
Gravity, also called gravitation, is a force that exists among all material objects in the universe. For
any two objects or particles having nonzero mass , the force of gravity tends to attract them toward
each other. Gravity operates on objects of all sizes, from subatomic particles to clusters of galaxies.
It also operates over all distances, no matter how small or great.
Newton ‘s law of gravitation states that the force of attraction between particles is directly
proportional to their mass and inversely proportional to the square of distance apart.
F ∝ m 1 m2
Gm1 m 2
F= −
r2
Where G is the universal gravitational constant,
G = 6.673 × 10-11m3kg-1s-2
Gravitational Field Strength
A gravitational field is a region where gravitational force acts on massive bodies.
Eg . gravitational field of the Earth.
The gravitational field strength tells us how strong a gravitational field is. The gravitational
field strength of the Earth near its surface is 9.81m / s2.
The gravitational field strength , E at a point is the force of gravity per unit mass exerted on a
mass placed.

2. The variation of the acceleration due to gravity g’ with distance r from the centre of the Earth
is illustrated by the graph above.
bove.
Gravitational Potential
The strength of the gravitational force at a point in a gravitational field is described by the
gravitational field strength E or g is a vector quantity.
Another quantity associated with the point in the gravitational field is the gravitational
potential. It is a scalar quantity
quantity.
The gravitational potential V at a point P in a gravitational field is defined as the work done
per unit mass to bring a body from infinity to P. The unit for gravitational potential is Jkg¯¹.
ody . Jkg
The gravitational potential energy U of a body at a point P in a gravitational field is defined as
the work done to bring the body from infinity to P. The unit for gravitational potential energy
.
is J.
Hence the gravitational potential energy U of a body of mass m at a point where the
gravitational potential, V is given by
U = mV
On the surface on the Earth, r = R
– Gravitational potential, V = -
otential,
– Gravitational potential energy, U = -
– The graph illustrates the variation of the gravitational potential V with distance r from the
centre of the Earth.

3. Relationship Between g and G
- G is the Universal Gravitational Constant.
- It is a scalar quantity with dimension L3M-1T-2
- g is the acceleration due to gravity .
vity
- It is a vector quantity with dimension LT-1
GMm
F=
R2
GMm
mg =
R2
GM
g= 2
R
gR2 = GM
Where g = acceleration due to gravity
R = constant radius of earth
G = universal gravitational constant
M = mass of Earth
Satellite Motion in Circular Orbits
Satellite is a body that revolves round a planet. Satellites can be categorized as natural satellites or
s
man-made satellites. The moon, the planets and comets are examples of natural satellites.
made
Examples of man-made satellites are Sputnik I , Measat I ,II and III whi are communication
made which
satellites. In order to launch satellite into orbit , rockets are used. When rocket that carries the
satellite reaches the required height , the satellite is launched into circular orbit with a certain
velocity v that is tangential to intended orbit.
o

4. question, solution:
Lets see this question, Try to solve on your own and then look at the solution:
Que. Suppose the earth increases its speed of rotation. At what new time period will the weight of
a body in the equator becomes zero ?
(Take g = 10 m/s2 and RE= 6400 km)
Solution:
The weight will become zero when g' = 0
also g' = g - Rw2
=> g - Rw2
=0
g
=> w =
R
2π g
=
T R
T = 1.4 hr
you’
I hope you’ll enjoyed studying Gravitation Chapter.