Question

Give the relation between g and G.

Gravitational force

Class:- 11th

Answer 1

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 N.m2.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/r2, 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/r2, or g = GM/r2 g is a constant at a given location, which depends upon M and r.)

Answer 2

$\huge\bold{Relation\: between\: g\: and\: G}$
________________________________

Let the Earth as a perfect sphere of mass M, radius R and centre(O).

F = $\dfrac{Gm_1m_2}{r^{2}}$ ....(1)

This force is responsible for the acceleration experienced by the body lying on the surface.

Then from Newton second law of motion,

F = mg.......... (2)

So,

From eq(1) and (2) we get,

mg = $\dfrac{GmM}{R^{2}}$

m cancelled from both sides

then we get,

g = $\dfrac{GM}{R^{2}}$

-:SOME MORE INFORMATION:-

=> Value of ‘g ’ depends upon mass of planets and stars.

=> Value of ‘g’ is independent of mass, shape or size of a body on which acceleration is produced.
__________________________________

⭐HOPE IT HELPS YOU OUT⭐