Module No. 11

1
Module # 11
Inertia & Gravity
Inertia
The property of body which opposes any change in its state of
rest or motion is called inertia. In other words, “Inertia is the
tendency of an object to resist a change in its state of rest or of
uniform motion."
OR
The property of matter that keeps an object in its state of rest or of
uniform motion and resists any effort to change its state of rest or
motion is called inertia.
Factors on which Inertia depends
The inertia of a body is directly proportional to the mass of the
body. It means that it is more difficult to change the state of rest or
of uniform motion of a body of large mass than that of lighter
bodies. This shows that if mass of body is less then its inertia will
be less i.e. Inertia of a body depends upon the mass of a body.

2
Examples
When a fast moving cyclist applies brakes suddenly, he falls
forward because the lower part of his body stops with the bicycle
but the upper part continues its motion.
If a car or a bus suddenly starts moving, a person sitting in it
would fall backward. This is because the body of the person in
contact with seat of the car or that of the bus is carried forward by
the motion of the car or the bus. The upper free part of the body
of the person remains at rest due to inertia and so the person falls
in the backward direction. Reverse will be the case when the
moving car or the bus suddenly stops. The person falls forward.
Law of Inertia
Newton's first law of motion is also called Law of Inertia.
Inertial Mass
The Inertial mass of a body is a measure of its reluctance to
change its state of motion when force is applied. F = mia,
therefore, mi = F/a, where mi is inertial mass. Thus, the type of
mass that appears in Newton's second law of motion is known as
inertial mass.

3
Frames of Reference
A system of coordinates (x,y,z) in which measurements are made
is called frame of reference. A room, an elevator or lift, a bus or a
compartment of a train, etc. are examples of frames of reference.
There are two kinds of frames of reference.
(1) Inertial Frame of Reference
(2) Non-inertial Frame of Reference
Inertial Frame of Reference
A frame of reference in which law of inertia is applied, or the
frame of reference which has no acceleration, is called inertial
frame of reference. Such frames may be at rest or may be moving
with uniform velocity. Newton's laws of motion are valid in inertial
frame.
Non-inertial Frame
When a frame of reference is moving with an accelerated
motion, it is called non-inertial frame. The laws of motion are not
valid in a system which is non-inertial.

4
Free Fall
Distance covered by a freely falling body in 2 seconds will be 19.6
m.
Force of Gravity
The unit of force of gravity in SI units is Newton.
Acceleration due to Gravity ‘g’
The acceleration produced in a freely falling body due to the
attraction of the earth is called acceleration due to gravity. It is
denoted by 'g'.
All the free falling bodies on the surface of earth move under the
gravitational force of earth. So, the gravitational force causes the
change in velocity of free falling bodies and the acceleration thus
produced is called gravitational acceleration or acceleration due
to gravity.
The value of g on the surface of earth is 9.8 m/s2
. As we go
higher, its value decreases.
Effect of Mass on Acceleration due to Gravity ‘g’
We know that g = GMe / R2

5
In this equation G, Me and R are constant for the earth. Relation of g
does not include mass of the falling body. Thus the value of g does
not depend upon the mass of the freely falling body.
Variation of ‘g’ with Altitude
It has been found that the mass of the earth Me is given by
Re
2
g
Me = ------------
G
OR
MeG
g = ----------- --------- (1)
Re
2
Since the values of 'Me' and 'G' are constant
1
g  -----------
Re
2
Thus the acceleration due to gravity is inversely proportional to
the square of the distance from the center of the earth. If the
distance from the center of the earth is increased, the value of g

6
will decrease. That is why the value of g at hills is lesser than the
value of g on the sea shore. If we go away from the surface of the
earth, a distance equal to the radius of the earth, the value of g
will become one fourth. Similarly, at a distance equal to twice the
radius of the earth from its surface, its value will decrease to one
ninth.
As the earth is nearly a sphere, so, the value of the radius of the
earth Re is almost constant on the surface of the earth and we
may, therefore, conclude safely that the value of 'g' is almost the
same all over its surface. But, contrary to be on the surface of the
earth, as we go up in space, the distance from the center of the
earth increases as is shown in the figure below.
Fig: Variation of g with altitude
If station A is located at a height h from the surface of the earth,
then, its distance from the center of the earth is (Re + h), and so,
the value of g at A is

7
MeG
gh = ------------- ------ (2)
(Re + h) 2
By dividing eq. (2) by eq. (1), we get
gh Re
2
------ = ----------------
g (Re + h)2
OR
Re
2
gh = g -----------------
(Re + h) 2
.
1
= g -----------------------
[1 + h/Re] 2
= g [1 + h/Re]-2
Using algebraic method (binomial expansion) and assuming h 
Re and thus ignoring the high powers of h/Re, we get

8
gh = g [1 - 2h/Re]
= g – 2gh/Re --------- (3)
Eq. (3) tells us that as we go up above the surface of the earth,
we find the value of g decreasing by an amount 2gh/Re. For
example, in going up by
16 km (= 16000 meters)
from the earth's surface, the value of h/Re is
16000m/6400000m =1/400
OR
gh = 9.8 – (9.8 x 2)/400 = 9.75 ms-2
Thus, near the earth's surface, the value of g is almost constant,
while, at higher altitudes, g decreases gradually.
Variation of ‘g’ at Equator and Poles
The value of g at the poles is greater than at equator because the
earth is not a perfect sphere. Its equatorial radius is greater than
the radius at poles.
Motion under Gravity
Following are the important points for the bodies falling under
gravity.

9
1 Bodies falling freely have initial velocity equal to Zero and
their acceleration is positive.
2 All objects thrown vertically upward have negative
acceleration equal to - 9.8 ms-2
and at the highest point their final
velocity becomes Zero.
3 When an object is thrown vertically upward, then, at the
highest point its final velocity becomes Zero. But, when, this
object returns to the earth, then, this final velocity becomes equal
to the initial Velocity. Thus its initial velocity will be Zero.
Gravitational Mass
The gravitational mass multiplied by g is the measure of the pull
exerted by the earth on the body.
Mathematically, this is expressed as follows:
w = mg x g
i.e., mg = w / g
Here, mg represents gravitational mass.
Gravitational Work
The space or region around the earth within which gravitational
force acts on a body is called gravitational field. The work done in

10
moving a body from one place to another under the action of
gravity is called gravitational work. It is found that
(1) The gravitational work in a closed path is zero, and
(2) The gravitational work is independent of the path followed by
the body.
Gravitational Field
The space or region around the earth within which a body can
experience a force of attraction due to the earth is called the
gravitational field.
The force acting on the body in the gravitational field at any point
of its path is equal to its weight W.
The work done in a gravitational field is independent of the path
followed by the body and the total work done in moving a body
along a closed path in a gravitational field is always equal to zero.
A field satisfying this condition, i.e. a field in which work done
along a closed path is zero and is independent of the path
followed, is known as conservative field. Thus gravitational field is
a conservative field. Other examples of conservative fields are
electrostatic and magnetic fields.

11
Artificial Gravity
We know that the astronaut orbiting around the earth is in the
state of weightlessness. There will be no force pressing him to
any side of the space ship. If the satellite is a space laboratory,
designed to stay in orbit for an extended period of time, then, this
"weightlessness" may be a severe handicap to the astronaut in
carrying out his laboratory duties, making observations and
performing experiments. In order to avoid this problem, an
"artificial gravity" can be created in the space station which will
permit the inhabitants to function in almost normal manner. All
that is required for this purpose is to set the space station into
rotation around its own axis with a certain frequency which can
provide the necessary centripetal force equal to the force of
gravity at that point.
These bodies tend to fall freely due to gravitational pull of earth.
This means that the satellite, the astronaut and every object in the
satellite are free falling bodies. Due to the tangential and
downward forces, these objects move along a curved path. The
curvature of this path is such that the earth curves around by the
same amount as the moving object and therefore does not touch
the surface of the earth.

Module No. 11

More Related Content

What's hot (20)

Similar to Module No. 11 (20)

More from Rajput AbdulWaheed Bhatti (20)

Recently uploaded (20)

Module No. 11