How is G and g are related?

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

$g = \frac{G M}{R^{3}}$

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

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

answer is D.

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Detailed Solution

Discover the equation that describes the force between two large objects by studying the general law of gravitation. Discover the free-falling object's acceleration caused by gravity. Discover the connection between these two by comparing them.

The gravitational acceleration is denoted by g, while the gravitational constant is denoted by G.
Relationship: The gravitational force exerted by one mass on another M is $F_{g} = \frac{GMm}{R^{2}}$ , where R denotes the separation of the bodies.
Let g represent the acceleration caused by this gravitational force for mass m.
Then, $F_{g} = m g$
$∴ mg = \frac{GMm}{R^{2}} \Rightarrow g = \frac{GM}{R^{2}}$ , here is how g and G are related..