Question

how is acceleration due to gravity (g) related to the gravitational constant (G) please guys explain it ☺☺​

Answer 1

Answer:

G stands for Newton's universal gravitational constant, whereas g stands for the acceleration due to gravity at a certain point.

G = 6.67300 × 10^(-11) Nm^2/kg^2. G is a constant throughout space and time.

g = 9.8 m/s^2 . g is a variable quantity.

G is a scalar quantity whereas g is a vector qualtity.  

 

(According to Newton's law of universal gravitation the force of attraction between two bodies is given by F = GMm/r^2, where the symbols stand for their usual well known meanings. Also the weight of a body of mass m is F = mg.

So mg = GMm/r^2, or g = GM/r^2

g is a constant at a given location, which depends upon M and r.)

Explanation:

G is the force between two bodies of unit mass separated by a unit distance is known as universal gravitational constant.

Whereas,

g is the acceleration produced in a body falling freely under the action of gravitational pull of the Earth is known as acceleration due to gravity or g.

From universal law of gravitation of Newton

We know that

F=Gm1m2/r^2

But, F=mg

Therefore, mg=Gm1m2/r^2

Here, m and m cancel from both sides

So, the eqn. Becomes

g = GM=R^2

G is the Force between genrally two heavenly bodies whereas ,

g is the force exerted by the planet on the object.