Physics, 29.01.2020 07:59, jhenifelix

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.

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answered: sharonbullock9558

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 . Now, if the distance between the two bodies is tripled of its initial distance, then the new separation becomes .

Substitute ${f_0}$ for ${F_1}$ , ${f_1}$ for ${F_2}$ , for ${r_1}$ and 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:

1. Calculate the total force on the earth due to Venus, Jupiter, and Saturn

2. How far must you compress a spring with twice the spring constant to store the same amount of energy

3. Choose the 200 kg refrigerator. Set the applied force to 400 N

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.

answered: Guest

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