Respuesta :
f1 = f0/9
The gravitational force between two points is described as
F = G*m1*m2/r^2
where
F = Force
G = Gravitational constant
m1, m2 = masses
r = distance between centers of masses
Since everything is remaining constant except r, we can ignore their actual values and simply compare the value of 1/r^2 and 1/(3r)^2. So let's do so:
1/(3r)^2 / 1/r^2 = 1/(3r)^2 * r^2/1 = r^2/(3r)^2 = r^2/(9r^2) = 1/9
So the value of f1 will be one ninth of the value of f0, giving f1 = f0/9
The new gravitational force of attraction after increasing the separation between the two particles is [tex]\boxed{\frac{{{f_0}}}{9}}[/tex] .
Further Explanation:
The gravitational force of attraction is the force which exists between each and every body. This force is explained by the Newton’s law of gravitation.
The Newton’s law of gravitation states that the force of attraction between the two bodies is directly proportional to the product of the masses of the two bodies and inversely proportional to the square of the distance between the two bodies.
It is expressed mathematically as:
[tex]F=\frac{{G{m_1}{m_2}}}{{{r^2}}}[/tex]
The above expression shows that the gravitational force is inversely proportional to the square of the distance between two bodies.
[tex]\begin{aligned}F&\propto \frac{1}{{{r^2}}}\hfill\\\frac{{{F_2}}}{{{F_1}}}&=\frac{{r_1^2}}{{r_2^2}}\hfill\\\end{aligned}[/tex]
If the distance between the two bodies is increased to thrice of its initial distance, the new distance becomes [tex]3r[/tex] .
Substitute [tex]{f_0}[/tex] for [tex]{F_1}[/tex] , [tex]{f_1}[/tex] for [tex]{F_2}[/tex] , [tex]r[/tex] for [tex]{r_1}[/tex] and [tex]3r[/tex] for [tex]{r_2}[/tex] in above expression.
[tex]\begin{aligned}\frac{{{f_1}}}{{{f_0}}}&=\frac{{{r^2}}}{{9{r^2}}}\hfill\\{f_1}&=\frac{{{f_0}}}{9}\hfill\\\end{aligned}[/tex]
Thus, the new gravitational force of attraction after increasing the separation between the two particles is [tex]\boxed{\frac{{{f_0}}}{9}}[/tex] .
Learn More:
1. Choose the 200 kg refrigerator. Set the applied force to 400 N https://brainly.com/question/4033012
2. Calculate the total force on the earth due to Venus, Jupiter, and Saturn https://brainly.com/question/2887352
3. How far must you compress a spring with twice the spring constant to store the same amount of energy https://brainly.com/question/2114706
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.
