MASS AND WEIGHT
Mass
We have learnt in the previous chapter that the mass of an object is the measure of its inertia (section 9.3). We have also learnt that greater the mass, the greater is the inertia. It remains the same whether the object is on the earth, the moon or even in outer space. Thus, the mass of an object is constant and does not change from place to place.
Weight
We know that the earth attracts every object with a certain force and this force depends on the mass (m) of the object and the acceleration due to the gravity (g). The weight of an object is the force with which it is attracted towards the earth.
We know that
F = m\(\times\) a, _____ (10.13)
that is,
F = m \(\times\) g. _____ (10.14)
The force of attraction of the earth on an object is known as the weight of the object. It is denoted by W. Substituting the same in Eq. (10.14), we have
W = m \(\times\) g _____ (10.15)
As the weight of an object is the force with which it is attracted towards the earth, the SI unit of weight is the same as that of force, that is, newton (N). The weight is a force acting vertically downwards; it has both magnitude and direction.
We have learnt that the value of g is constant at a given place. Therefore at a given place, the weight of an object is directly proportional to the mass, say m, of the object, that is, W \(\propto\) m. It is due to this reason that at a given place, we can use the weight of an object as a measure of its mass. The mass of an object remains the same everywhere, that is, on the earth and on any planet whereas its weight depends on its location because g depends on location.
Source: This topic is taken from NCERT TEXTBOOK
WEIGHT OF AN OBJECT ON THE MOON
We have learnt that the weight of an object on the earth is the force with which the earth attracts the object. In the same way, the weight of an object on the moon is the force with which the moon attracts that object. The mass of the moon is less than that of the earth. Due to this the moon exerts lesser force of attraction on objects.
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
\(W_m=G\frac{M_m\times m}{R_m^2}\) _____ (10.16)
Let the weight of the same object on the earth be We. The mass of the earth is M and its radius is R
|
Celestial body |
Mass (kg) |
Radius (m) |
|
Earth |
5.98 × 1024 |
6.37 × 106 |
|
Moon |
7.36 × 1022 |
1.74 × 106 |
Table 10.1:
\(g=G\frac{M}{R^2}\) _____ (10.9)
\(W=m\times g\) _____ (10.15)
From Eqs. (10.9) and (10.15) we have
\(W_e=G\frac{M\times m}{R^2}\) _____ (10.17)
Substituting the values from Table 10.1 in Eqs. (10.16) and (10.17), we get
\(W_m=G\frac{7.36\times 10^{22}kg\times m}{(1.74\times 10^6m)^2}\)
\(W_m=2.431\times 10^{10}G\times m\) _____ (10.18(a))
\(W_e=1.474\times 10^{11}G\times m\) _____ (10.18(b))
Dividing Eq. (10.18a) by Eq. (10.18b), we get
\(\frac{W_m}{W_e}=\frac{2.431\times 10^{10}}{1.474\times 10^{11}}\)
\(\frac{W_m}{W_e}=0.165\approx\frac{1}{6}\) _____ (10.19)
Weight of the object on the moon = (1/6) \(\times\) its weight on the earth.
Illustration 10.4:
Mass of an object is 10 kg. What is its weight on the earth?
Sol:
Mass, m = 10 kg
Acceleration due to gravity, g = 9.8 m s–2
W = m \(\times\) g
W = 10 kg \(\times\) 9.8 ms-2 = 98 N
Thus, the weight of the object is 98N.
Illustration 10.5:
An object weighs 10 N when measured on the surface of the earth. What would be its weight when measured on the surface of the moon?
Sol:
We know,
Weight of object on the moon = (1/6) \(\times\) its weight on the earth.
That is,
\(W_m=\frac{W_e}{6}=\frac{10}{6}\)
= 1.67 N.
Thus, the weight of object on the surface of the moon would be 1.67 N.
Questions
1. What are the differences between the mass of an object and its weight?
2. Why is the weight of an object on the moon \(\frac{1}{6}^{th}\) its weight on the earth?
Source: This topic is taken from NCERT TEXTBOOK