10.2.1 TO CALCULATE THE VALUE OF 9
To calculate the value of g, we should put
the values of G, M and R in Eq. (10.9),
namely, universal gravitational constant,
G = 6.7 x 10-11 N m2 kg-2, mass of the earth,
M = 6 x 1024 kg, and radius of the earth,
R= 6.4 x 106 m.
M
9 = G
R?
6.7x10'll N m² kg 2 x6x1024 kg
(6.4x10 m)?
= 9.8 m s-2.
Answers
Explanation:
Every object in the universe attracts every other object with a force which is proportional to the product of their masses and inversely proportional to the square of the distance between them. The force is along the line joining the centers of two objects.
Universal Law of Gravitation
Let two objects A and B of masses M and m lie at a distance d from each other as shown in Fig. 10.2. Let the force of attraction between two objects be F. According to the universal law of gravitation, the force between two objects is directly proportional to the product of their masses. That is,
F ∝ M × m (10.1)
And the force between two objects is inversely proportional to the square of the distance between them, that is,
F ∝ 1/d2 (10.2)
combining Eqs. (10.1) and (10.2), we get
F ∝ M m/d2 (10.3)
or F = G M × m / d2 (10.4)
where G is the constant of proportionality and is called the universal gravitation constant. By multiplying crosswise, Eq. (10.4) gives
F × d2 = G M × m
or G= F d2 / M ×m (10.5)
The SI unit of G can be obtained by substituting the units of force, distance and mass in Eq. (10.5) as N m2 kg-2.
The value of G was found out by Henry Cavendish (1731 – 1810) by using a sensitive balance. The accepted value of G is 6.673 × 10-11 N m2 kg-2.
We know that there exists a force of attraction between any two objects. Compute the value of this force between you and your friend sitting closeby. Conclude how you do not experience this force!
10.1.2 IMPORTANCE OF THE UNIVERSAL LAW OF GRAVITATION
The universal law of gravitation successfully explained several phenomena which were believed to be unconnected:
i. the force that binds us to the earth;
ii. the motion of the moon around the earth
iii. the motion of planets around the Sun and
iv. the tides due to the moon and the Sun.
To calculate the value of g, we should put the values of G, M and R in Eq. (10.9), namely, universal gravitational constant, G = 6.7 × 10-11 N m2 kg-2, mass of the earth, M = 6 × 1024 kg, and radius of the earth, R = 6.4 × 106 m. = 9.8 ms-2