define acceleration due to gravity give 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.
Explanation:
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ANSWER :-
What is Acceleration due to Gravity?
→ Acceleration due to gravity is the acceleration gained by an object due to gravitational force. Its SI unit is m/s2. It has both magnitude and direction, hence, it’s a vector quantity. Acceleration due to gravity is represented by g. The standard value of g on the surface of the earth at sea level is 9.8 m/s2.
Relation between g and G :-
→ 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. That means they are independent entities.
In physics, G and g can be related mathematically as –
g = GM/R²
Where,
g is the acceleration due to the gravity of any massive body measured in m/s2.
G is the universal gravitational constant measured in Nm2/kg2.
R is the radius of the massive body measured in km.
M is the mass of the massive body measured in Kg
G and g relation
→ 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.
★ g = The acceleration experienced by a body under free fall due to the gravitational force of the massive body. It changes from place to place.
Acceleration due to gravity of the earth is
9.8 m/s2
★ G = Universal Gravitational Constant. 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
According to the universal law of gravit,
F = GMm/R² ————(1)
From Newton’s second law of motion we can write –
g = Fm ———–(2)
Substituting equation (1) in (2) we get-
g = GMm/R²m
Thus, we arrive at the g formula in physics as –