Question

arrive at the relation between acceleration due gravity and universal gravitational constant G​

Answer 1

Answer:

$g = G\frac{M}{R^2}$

Explanation:

According to Newton's universal law of gravity,

$F = G \frac{Mm}{R^2}$

According to Newton's second law of motion,

$F = ma$

   = $mg$     (when a body is freely falling under gravity)

Equating the two equations we get:

$G \frac{Mm}{R^2}$ = $mg$

=> $g = G\frac{M}{R^2}$

g =  acceleration due to the gravity

G = universal gravitational constant

R = radius of the massive body

M = mass of the massive body

m = mass of small body