To know the basic difference between g and G we need to understand their meanings, definitions, and the relation between them. We will learn their SI units and formulae also.
'g' - Meaning and Definition
‘g‘ is the symbol denoting acceleration due to gravity.
So, basically ‘g‘ is a kind of acceleration produced due to the gravity of any celestial body. Any celestial body having huge mass attracts an object towards its center. This force of attraction is called gravity.
Higher the mass of a celestial body higher will be the value of acceleration due to gravity.
A freely falling object starts accelerating under the gravitational pull of the earth. We denote this acceleration as ‘g‘.
SI Unit of g
The SI unit of g (acceleration due to gravity) is equal to m/s2, which is, obviously, the same as acceleration.
Value of g
As mentioned above, higher the mass of an object higher will be the value of acceleration due to gravity on its surface. It implies that the value of ‘g’ is not the same at every place. It varies from the planet to the planet or the star to the star.
The value of g at different celestial bodies:
Sun: 274 m/s2
Moon: 1.625 m/s2
Earth: 9.8 m/s2 on poles and 9.78 m/s2 on equator
Jupiter: 24.92 m/s2
Effects and Examples of g
An interesting effect emerges from the fact that the value of acceleration due to gravity on earth is 9.8 m/s2. If a leather ball and a plastic ball is dropped from the same height, which would you think to touch the ground first?
Yes, both will touch the ground at the same time. (neglecting the effect of air resistance)
The reason is:
as we know that, a = v/t (Where a = acceleration, v= velocity, and t = time)
So, if the acceleration is the same then the ratio of their velocity is to time will be the same. The value of ‘g’ = 9.8 m/s2 for both of the different balls. Hence, the velocities and time taken would be equal.
Formula of g
According to Newton’s second law of motion, the acceleration of an object is equal to the force acting upon that object divided by the mass of that object. Therefore, we can write:
a = F/m
(Where a = acceleration F = net force acting upon that object, and m = mass of that object.)
Similarly, We can write:-
The value of g = F/m _____________(i)
‘g’ is a vector quantity. It means, it has both magnitude as well as the direction.
'G' - Meaning and Definition
‘G’ is the symbol denoting ‘gravitational constant‘. This is also known as universal gravitational constant.
The gravitational constant is equal to the force of attraction between the two objects of unit mass separated by the unit distance.
We will learn about it in detail below while deriving the equation (vi).
‘G’ is a scalar quantity. It means, it has only magnitude and no direction.
SI Unit of G
The SI unit of ‘G‘ is equal to:- Nm2/ kg2
Value of G
Value of ‘G‘ is equal to : 6.67 × 10-11 Nm2/ kg2
Effects and examples of G
Due to the gravity, or gravitation:
We are able to move around on the earth.
The drops of the rain, fall on the earth.
The earth is able to hold its atmosphere with all the gases intact. The gases are not flying away from the earth’s surface because of the effect of the earth’s gravitational force.
The gravitational pull of the moon creates tides on the earth.
The moon rotates around the earth, and the earth rotates around the Sun.
Formula of G
As per Newton’s law of universal gravitation:
Every object in the universe attracts every other object with a certain force (F). The value of that force is:
Proportional to the product of their masses (m1 × m2)
Inversely proportional to the square of the distance between them (r2)
(Where m1 and m2 are the masses of these objects and r is the distance between them.)
Therefore, we can write:
F ∝ (m1 × m2) _____________(ii)
and F ∝ 1/r2 _____________(iii)
Combining both of these equations, we can write:
F ∝ m1 × m2/ r2
to remove the sign of proportionality(∝) a constant is used that is called ‘G’.
Hence, F = G × (m1 × m2)/ r2 _____________(iv)
The value of ‘G’ remains constant at every place in the universe. This is why it is called a universal constant.
The equation (iv) can be written as:
G = F × r2 / (m1 × m2) _____________(v)
If m1 = m2 = 1 and r = 1 then the equation (v) will become:
G = F _____________(vi)
Relation between g and G
From equation (i) above, the value of ‘g’ is:-
g = F/m1 ____________(i)
and from the equation (v) we can write the value of ‘G’ as:
G = F × r2 / (m1 × m2)____________(ii)
Putting the value of F = mg from Equation (i) into the equation (ii) we get,
g = GM/R2
Difference between g and G
Here are the 4 must-know difference between g and G.
|It is an acceleration due to gravity.||It is the gravitational constant.|
|Its value varies as per the mass of the objects.||Its value remains constant at every place in the universe.|
|It is a vector quantity.||It is a scalar quantity.|
|Its value of earth is 9.8 m/s2 on poles and 9.78 m/s2 on the equator.||Its value is 6.67 × 10-11 Nm2/ kg2 at every place in the universe.|