Question

Two particles are separated by a certain distance. the force of gravitational interaction between them is f0. now the separation between the particles is tripled. find the new force of gravitational interaction f1.

Answer 1

The gravitational force after the separation between the two particles is tripled will be $\boxed{\frac{{{f_0}}}{9}}$ .

Further Explanation:

The force of attraction due to gravity is the force which exists between two bodies kept at a distance from each other. This force is given by Newton’s law of gravitation.

The Newton’s law of gravitation states that the gravitational force of attraction between the bodies kept at a certain distance is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

The above explanation can be shown mathematically as:

$\begin{aligned}F&\propto\frac{1}{{{r^2}}}\hfill\\\frac{{{F_2}}}{{{F_1}}}&=\frac{{r_1^2}}{{r_2^2}}\hfill\\\end{aligned}$

The proportionality equations can be combined and the formula for the Gravitational force of attraction can be written as:

$F=\frac{{G{m_1}{m_2}}}{{{r^2}}}$

Let us consider that in initial distance between the two bodies is $r$ . Now, if the distance between the two bodies is tripled of its initial distance, then the new separation becomes $3r$.

Substitute ${f_0}$  for ${F_1}$ , ${f_1}$  for ${F_2}$ , $r$ for ${r_1}$  and $3r$  for ${r_2}$  in above expression.

$\begin{aligned}\frac{{{f_1}}}{{{f_0}}}&=\frac{{{r^2}}}{{{{\left({3r}\right)}^2}}}\hfill\\{f_1}&=\frac{{{f_0}}}{9}\hfill\\\end{aligned}$

Thus, the new gravitational force of attraction after increasing the separation between the two particles is $\boxed{\frac{{{f_0}}}{9}}$ .

Learn More:

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2. How far must you compress a spring with twice the spring constant to store the same amount of energy brainly.com/question/2114706

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Answer Details:

Grade: Senior School

Subject: Physics

Chapter: Gravitation

Keywords:

Gravitational interaction, separated by a certain distance, gravitational force, Newton’s law of gravitation, between the particles, tripled.

Answer 2

 as i recall, gravity is relative to the square of the distance. 

so if the distance is tripled, then the gravitational attraction would be reduced by 3^2 or 1/9. 
so F1 = F0/9 


if the satellite is 2R from the center, and is moved to 4R (doubled would be 3R, tripled is 4R) then the distance is twice, and gravity would be 2^2 or 1/4.