Question

Gunnie ✌️
Chapter :- gravitation
How is G related with g?

where :-
g = acceleration due to Gravity
G = Universal Gravitational constant

Please Explain with proper explanation :)

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#No copy paste​

Answer 1

Let ,

• M = mass of the earth
• R = radius of the earth
• m = mass of the object placed on the surface of the earth
• g = acceleration due to gravity

The weight of the object is equal to gravitaional force acting on it on the surface of the earth

$\rightarrow \displaystyle \mathtt{F = mg}....(1)$

By Newton's Law of gravitation ,

$\rightarrow \displaystyle \mathtt{F = \frac{G \: M \: m}{ {R}^{2} } }....(2)$

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

$\rightarrow \displaystyle \mathtt{mg = \frac{G \: M \: m}{ {R}^{2} } }$

$\displaystyle \boxed {\red{\mathtt{g = \frac{G \: M \: }{ {R}^{2} } }}}$

Additional information

when the object of mass( m) is taken to height (h) above the surface of earth , the acceleration due to gravity acting on it is (g h)

weight of the object

$\rightarrow \displaystyle \mathtt{F = mg_h}....(3)$

Gravitational force acting on the body at height h above the surface of earth ,

$\rightarrow \displaystyle \mathtt{F = \frac{G \: M \: m}{ {(R + h)}^{2} } }....(4)$

From equation (3) and (4) we get ,

$\rightarrow \displaystyle \mathtt{mg_h = \frac{G \: M \: m}{ {(R + h)}^{2} } }$

$\displaystyle \boxed {\green{\mathtt{g_h = \frac{G \: M \: }{ {(R + h)}^{2} } }}}$

Answer 2

Answer:

See to my attachment.

Hope it will help you.