Question

Derive the relation between G and g. Name the factors on which g depends.

Answer 1

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★DERIVATION★

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.

✯G and g✯

In physics, G and g can be related mathematically as –

g=GMR2

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.

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/kg2Swipe left

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

Hope you understood the relation and conversion between G and g along with formula, definition, difference, and values.