Page 112 - Understanding NCERT Science 09

In the absence of this force, the stone flies off 9.1.1 UNIVERSAL LAW OF GRAVITATION
along a straight line. This straight line will be
a tangent to the circular path. Every object in the universe attracts every
other object with a force which is proportional
to the product of their masses and inversely
Tangent to a circle
proportional to the square of the distance
between them. The force is along the line
joining the centres of two objects.
More to know

A straight line that meets the circle at
one and only one point is called a
F = G Mm
tangent to the circle. Straight line d 2
ABC is a tangent to the circle at
point B.
Fig. 9.2: The gravitational force between two
uniform objects is directed along the line
The motion of the moon around the earth joining their centres.
is due to the centripetal force. The centripetal
force is provided by the force of attraction of Let two objects A and B of masses M and
the earth. If there were no such force, the m lie at a distance d from each other as shown
moon would pursue a uniform straight line in Fig. 9.2. Let the force of attraction between
motion. two objects be F. According to the universal
It is seen that a falling apple is attracted law of gravitation, the force between two
towards the earth. Does the apple attract the objects is directly proportional to the product
earth? If so, we do not see the earth moving of their masses. That is,
towards an apple. Why? F µ M × m (9.1)
According to the third law of motion, the And the force between two objects is inversely
apple does attract the earth. But according proportional to the square of the distance
to the second law of motion, for a given force, between them, that is,
acceleration is inversely proportional to the
mass of an object [Eq. (8.4)]. The mass of an 1
apple is negligibly small compared to that of F µ 2 (9.2)
d
the earth. So, we do not see the earth moving
towards the apple. Extend the same argument Combining Eqs. (10.1) and (10.2), we get
for why the earth does not move towards the
moon. M ´m
In our solar system, all the planets go F µ d 2 (9.3)
around the Sun. By arguing the same way,
we can say that there exists a force between M × m
the Sun and the planets. From the above facts or, F = G 2 (9.4)
d
Newton concluded that not only does the
earth attract an apple and the moon, but all where G is the constant of proportionality and
objects in the universe attract each other. This is called the universal gravitation constant.
force of attraction between objects is called By multiplying crosswise, Eq. (9.4) gives
the gravitational force. F × d = G M × m
2

GRAVITATION 101

Rationalised 2023-24