Page 113 - Understanding NCERT Science 09

2 From Eq. (9.4), the force exerted by the
F d
or G = (9.5) earth on the moon is
M ´m
M × m
The SI unit of G can be obtained by F = G 2
d
substituting the units of force, distance and
2
–2
2
mass in Eq. (9.5) as N m kg . 6.7 10 - 11 N m kg -2 ´ 6 10 24 kg 7.4 10 22 kg
´
´
´
´
=
The value of G was found out by (3.84 10 m) 2
8
´
Henry Cavendish (1731 – 1810) by using a
20
= 2.02 × 10 N.
sensitive balance. The accepted value of G is
2
–2
6.673 × 10 –11 N m kg . Thus, the force exerted by the earth on
20
We know that there exists a force of the moon is 2.02 × 10 N.
attraction between any two objects. Compute
the value of this force between you and your uestions
the bodies are big or small, whether Q 2. Write the formula to find the
friend sitting closeby. Conclude how you do
not experience this force! 1. State the universal law of
gravitation.
The law is universal in the sense that
magnitude of the gravitational
it is applicable to all bodies, whether
force between the earth and an
object on the surface of the earth.
More to know they are celestial or terrestrial. 9.1.2 IMPORTANCE OF THE UNIVERSAL
Inverse-square
LAW OF GRAVITATION
is
inversely
F
that
Saying
The universal law of gravitation successfully
proportional to the square of d
explained several phenomena which were
gets
means, for example, that if d
becomes
bigger by a factor of 6, F
believed to be unconnected:
(i) the force that binds us to the earth;
1
times smaller. (ii) the motion of the moon around the
36
earth;
(iii) the motion of planets around the Sun;
and
Example 9.1 The mass of the earth is (iv) the tides due to the moon and the Sun.
6 × 10 24 kg and that of the moon is
22
7.4 × 10 kg. If the distance between the 9.2 Free Fall
earth and the moon is 3.84×10 km,
5
calculate the force exerted by the earth on Let us try to understand the meaning of free
–11
2
-2
the moon. (Take G = 6.7 × 10 N m kg ) fall by performing this activity.
Activity ______________ 9.2
Solution:
24
The mass of the earth, M = 6 × 10 kg • Take a stone.
The mass of the moon, • Throw it upwards.
22
m = 7.4 × 10 kg • It reaches a certain height and then it
starts falling down.
The distance between the earth and the
moon, We have learnt that the earth attracts
d = 3.84 × 10 km objects towards it. This is due to the
5
5
= 3.84 × 10 × 1000 m gravitational force. Whenever objects fall
8
= 3.84 × 10 m towards the earth under this force alone, we
2
G = 6.7 × 10 –11 N m kg –2 say that the objects are in free fall. Is there any
102 SCIENCE
Rationalised 2023-24