Define acceleration due to gravity? And derive the relation between g and G?
Answers
Answer:
The acceleration on an object due to the gravity of any massive body is represented by g (small g). The force of attraction between any two unit masses separated by unit distance is called universal gravitational constant denoted by G(capital g). The relation between G and g is not proportional
Answer:
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Explanation:
Although there exists a formula to express the relation between g and G in physics. There is no correlation between acceleration due to gravity and universal gravitation constant, as the value of G is constant. The value of G is constant at any point in this universe. G and g are not dependent on each other.
What is G and g?
The G and g are distinct entities in physics. Below is the table of the difference between G and g.
Symbol Definition Nature of Value Unit
Acceleration due to gravity
g The acceleration experienced by a body under free fall due to the gravitational force of the massive body Changes from place to place.
Acceleration due to gravity of the earth is 9.8 m/s2
m/s2
Universal Gravitational Constant
G The force of attraction between two objects with unit mass separated by a unit distance at any part of this universe. Constant at any point in this universe.
G = 6.673×10-11 Nm2/kg2
Nm2/kg2
g Formula
According to the universal law of gravit,
F=GMmR2 ————(1)
From Newton’s second law of motion we can write –
g=Fm ———–(2)
Substituting equation (1) in (2) we get-
g=GMmR2m
Thus, we arrive at the g formula in physics as –
⇒g=GMR2