Question

Establish the relationship between acceleration due to gravity and universal gravitational constant

Answer 1

The relationship between G and g is:
g = GM / r^2

See the attachment for the explanation

HOPE IT HELPS..... :-)

Answer 2

Solution:

The earth's mass = M

The object's mass on earth = m

According to the equation,

$F=\frac{G M m}{r^{2}}$

Where,

r defines the distance between earth and the object and G is universal gravitational constant.

Here, F is the force applied by the Earth on the object and the object accelerates towards earth with an acceleration g (acceleration due to gravity)

Therefore, $F = mg$

On substituting F in above equation, we get,

$m g=F=\frac{G M m}{r^{2}}$

$\Rightarrow g=\frac{G M}{r^{2}}$