Page 116 - Understanding NCERT Science 09

9.3 Mass attracts the object. In the same way, the weight
of an object on the moon is the force with
We have learnt in the previous chapter that the which the moon attracts that object. The mass
mass of an object is the measure of its inertia . of the moon is less than that of the earth. Due
We have also learnt that greater the mass, the to this the moon exerts lesser force of attraction
greater is the inertia. It remains the same on objects.
whether the object is on the earth, the moon Let the mass of an object be m. Let its
or even in outer space. Thus, the mass of an weight on the moon be W . Let the mass of
m
object is constant and does not change from the moon be M and its radius be R .
m
m
place to place. By applying the universal law of
gravitation, the weight of the object on the
9.4 Weight moon will be
W m = G M m ´m (9.16)
We know that the earth attracts every object R m 2
with a certain force and this force depends on Let the weight of the same object on the
the mass (m) of the object and the acceleration earth be W . The mass of the earth is M and its
e
due to the gravity (g). The weight of an object radius is R.
is the force with which it is attracted towards
the earth. Table 9.1
We know that
F = m × a, (9.13) Celestial Mass (kg) Radius (m)
that is, body
F = m × g. (9.14) 24 6
The force of attraction of the earth on an Earth 5.98 × 10 6.37 ××10
object is known as the weight of the object. It Moon 7.36 ××10 22 1.74 ××10 6
is denoted by W. Substituting the same in Eq.
(9.14), we have
W = m × g (9.15) From Eqs. (9.9) and (9.15) we have,
As the weight of an object is the force with M ´m
W = G
which it is attracted towards the earth, the SI e R 2 (9.17)
unit of weight is the same as that of force, that Substituting the values from Table 10.1 in
is, newton (N). The weight is a force acting
vertically downwards; it has both magnitude Eqs. (9.16) and (9.17), we get
22
and direction. 7.36 10 kg ´m
´
We have learnt that the value of g is W m = G 6 ) 2
´
constant at a given place. Therefore at a given ( 1.74 10 m
place, the weight of an object is directly W m = 2.431 10 G × m (9.18a)
10
´
proportional to the mass, say m, of the object, 11 (9.18b)
´
that is, W µ m. It is due to this reason that at and W e = 1.474 10 G × m
a given place, we can use the weight of an Dividing Eq. (9.18a) by Eq. (9.18b), we get
object as a measure of its mass. The mass of W 2.431 10 10
an object remains the same everywhere, that m = ´ 11
´
is, on the earth and on any planet whereas its W e 1.474 10
weight depends on its location because g W 1
depends on location. or m = 0.165 ≈ (9.19)
W 6
e
9.4.1 WEIGHT OF AN OBJECT ON Weight of the object on the moon 1
=
THE MOON Weight of the object on theearth 6
We have learnt that the weight of an object on Weight of the object on the moon
the earth is the force with which the earth = (1/6) × its weight on the earth.

GRAVITATION 105

Rationalised 2023-24