PPT on Gravitation Cl 9

1. CHAPTER-10
GRAVITATION

5. The theory of gravitation was developed
by Albert Einstein at 1907 and 1915. At
the 20th century, Newton's Law of
Universal Gravitation was accepted by
all. According to Newton's gravitational
force is caused by matter. Gravitation is
nothing but a force which is exerted by
the surface of the earth.

6. GRAVITATION
movement, or a tendency to move, towards a centre
of gravity, as in the falling of bodies to the earth.
Earth attracts all things towards it through an unseen
force of attraction. This force of attraction is called as
gravitation or gravitational pull. You must have noticed
that every time you throw an object upwards, it reaches
a certain height and then falls down on the earth's
surface.

7. Gravitation Gravity
It may be an attractive force or repulsive force as well. It is always a kind of attractive force.
It is considered as the universal force.
It is not considered as the universal
force.
The direction of this gravitational force is along the
radial direction from the masses.
The direction of this force is along the
line joining the earth’s center and the
center of the body. It is always working
towards the center of the earth.
It is a very weak kind of force. It is a strong kind of force.
This force is a vector physical quantity.
Gravity force is having its own vector
field.
It needs objects with two masses It needs only one mass.
The force will be zero when the distance between
bodies is infinity.
The force of gravity will be zero at the
center of the earth.

9. Universal Law of Gravitation
Every object in the universe attracts
every other object with a force which
is proportional to the product of their
masses and inversely proportional to
the square of the distance between
them.
The force is along the line joining the
centres of two objects.

10. Let two objects A and B of masses M and m lie at a
distance d from each other as shown in Fig.
Let the force of attraction between two objects be F.
According to the universal law of gravitation, the
force between two objects is directly proportional to
the product of their masses. That is,
F Mxm

11. And the force between two objects is inversely
proportional to the square of the distance between
them, that is,
F α 1 ⁄ d2 ---------- (2)
Combining Eqs. (1) and (2), we get
F α Mm ⁄ d2 ---------- (3)
or, F = G (Mm) ⁄ d2) ----------
(4)
where G is the constant of proportionality and is calle
the universal gravitation constant. By multiplying
crosswise, Eq. (4) gives
F × d 2 = G Mm
or G = F d2/ Mm ---------- (5)

12.  The SI unit of G can be obtained by
substituting the units of force, distance and
mass in Eq. (5) as N m2 kg–2.
 The value of G was found out by Henry
Cavendish (1731 – 1810) by using a
sensitive balance. The accepted value of G
is 6.673 × 10–11 N m2 kg–2.
 We know that there exists a force of
attraction between any two objects.
Compute the value of this force between
you and your friend sitting closeby.

13. NUMERICALS ON UNIVERSAL LAW OF GRAVITATION
1) Determine the gravitational force if two masses are 30kg and 50kg
separated by a distance 4m.
G = 6.67259 x 10–11 N m2/kg2.
Solution:
Given:
m1 = 30 kg, m2 = 50 kg
r = 4m and
G = 6.67259 x 10–11 N m2/kg2.
Universal gravitation formula is given by,
= [6.673×10–11 ×30×50] / 16
F = 62.55 x 10–11N
H.W
2) Determine the gravitational force if the mass of two bodies are 80 kg
and 200 kg and they are separated by a distance of 6m.

14. What is the importance of universal law of
gravitation?
The importance of universal law of
gravitation lies in the fact that it was
successful in explaining many phenomena
such as:
how different objects in this universe
affect others
how gravity is responsible for the weight
of a body and keeps us on the ground
how lunar motion occurs around the
earth
how planetary motion takes place
how the tidal waves originate

15. What is free fall ?
Free fall is the term that is used to
describe a falling object that only has
gravity acting upon it. Free falling
objects accelerate at a rate of 9.8
m/s2.

16. ACCELERATION DUE TO GRAVITY ‘g’
 The acceleration produced in freely falling
body due to gravitational force is called
acceleration due to gravity.
 Acceleration due to gravity is represented by
letter 'g'.
 Value of g is 9.8 m/s2 .

17. Derivation of acceleration due to gravity ‘g’:
As per Newton's law, Force = mass × acceleration
= m×a ............... (1)
where m is mass and a is acceleration
Gravitational force acting on a mass m on earth's surface
= ..........................(2)
where G is Gravitational force constant, M is mass of
earth and R is radius of earth
By comparing (1) and (2), acceleration due to gravity
= g
=(G×M)/R2

18. TO CALCULATE THE VALUE OF ‘g’ - T.Bk Pg 135
Numericals based on acceleration due to gravity
Q.1
Calculate the acceleration due to gravity for an object placed at the
surface of the Earth, given that, the radius of the Moon is 1.74 × 106 m and
its mass is 7.35 × 1022 kg.
Solution:
The radius of the moon, r = 1.74 × 106m = 1740000 m
r2 = 3.0276 × 1012m
The mass of moon = 7.35 × 1022 kg
Using the formula for the acceleration due to gravity, we write,
g=GM/r2
Upon substituting the values, we get,
g=(6.673×10−11)(7.35×1022)/3.0276×1012g=(6.673×10−11)(7.35×102
2)/3.0276×1012g
= (4.905 ×1012)/(3.0276 × 1012)
g = 1.620 m/s2
The acceleration due to gravity is 1.620 m/s2.

19. Q.2
The radius of the Earth is 6.38 x 106 m. The mass of the Earth is 5.98x
1024 kg. If a satellite is orbiting the Earth 250 km above the surface, what
acceleration due to gravity does it experience?
Solution:
It can be seen that the satellite is present at a considerable height
from the surface of the Earth, hence the height cannot be
neglected. Using the first formula, we can write,
R=r+h = (6.38 x 106 m) + (250 km)
R = 6 380 000 + 250 000 m
R = 6 630 000 m
The acceleration due to the gravity of the satellite can be found
from the formula:
g=GM/(r+h)2 g=(6.673×10−11)(5.98×1024)/(6630000)2
g = (3.9704×1014)/(4.396×1013)
g= 9.031 m/s2

21. Mass of moon is lesser than that of earth. Due to this
the moon exerts lesser force of attraction on objects.
Hence weight of an object on the moon l/6th its weight
on the earth.
Why is the weight of an object on the moon 1/ 6 th its weight
on the earth?

22. WEIGHT OF AN OBJECT ON THE MOON
Let the mass of an object be m. Let its weight on the moon be
Wm. Let the mass of the moon be Mm and its radius be Rm. By
applying the universal law of gravitation, the weight of the object
on the moon will be
Let the weight of the same object on the earth be We. The
mass of earth is M and its radius is R.
(2)

23. Substituting the values in equations (1) and (2) we get
(4)
Dividing equation (3) by (4)

24. THRUST:
The force acting on an object perpendicular to the
surface is called thrust.
It is vector quantity
 SI Unit of thrust is Newton.
Examples of Thrust
• School bags have larger straps so that the
pressure exerted on shoulders is less.
• Cutting nails is an example of thrust.
• Sucking cool drink through a straw.
• Breathing
• Constructing a building.
• Pushing an empty vessel into the water, it
experiences the buoyant force.
• Pushing a cork into the water, it experiences the
buoyant force.

28. PRESSURE IN FLUIDS/FLUID PRESSURE
 Fluid pressure is a measurement of the force per unit area.
 Fluid pressure can be caused by gravity, acceleration, or forces in
a closed container.
 Since fluid has no definite shape, its pressure applies in all
directions
 To define fluid pressure, we can say that it is the pressure at a
point within a fluid arising due to the weight of the fluid.
 Pressure in liquids is equally divided in all directions
 Therefore if a force is applied to one point of the liquid, it will be
transmitted to all other points within the liquid.
 Points along the same depth will have the same pressure, while
points at different depths will have different pressure.
 The SI Unit (International System of Unit) of pressure is the Pascal,
or Newton per meter squared (N/m2).

29. BUOYANCY
An object that is partly, or completely submerged in a fluid
experiences a greater pressure on its bottom surface than on
its top surface. This causes a resultant force upwards. This
force is called upthrust, and is also known as buoyancy.
The upward force exerted by fluids (liquid and gas) on objects
when they are immersed in them is called buoyant force and the
phenomenon is called buoyancy. Now to keep the object
immersed we have to apply external force from upward
direction to overcome buoyant force.