Question

Differentiate between acceleration due to gravity and universal gravitational constant. Derive

a relation between ‘g’ and ‘G’.​

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 and it is a scalar quantity.

g = 9.8 m.s-2,   g is acceleration due to gravity which is a variable quantity and a vector qualtity. 

 

According to Newton's law of universal gravitation the force of attraction between two bodies is given by

F = GMm/r2 ---------- (i)

From Newton's second law of motion the weight of a body of mass m is

F = mg -----------------(ii)

From (i) and (ii)

mg = GMm/r2

or

g = GM/r2

Answer 2

g=

$\sqrt{ gm \div r}$