### Gravitational Equilibrium Problem#### Diagram Explanation:The diagram shows three planets:- **Planet #1 (Mass \( M_1 \))**: Positioned directly between Planet #2 and Planet #3.- **Planet #2 (Mass \( M_2 \))**: Located at the right end of the diagram.- **Planet #3 (Mass \( M_3 \))**: Located at the left end of the diagram.The distances are labeled as follows:- The distance between Planet #1 and Planet #2 is denoted as \( r \).- The distance between Planet #1 and Planet #3 is denoted as \( R - r \) (since the total distance \( R \) between Planet #2 and Planet #3 is given).#### Problem Statement:Planet #2 (mass \( M_2 \)) and Planet #3 (mass \( M_3 \)) are separated by distance \( R \). Planet #1 (mass \( M_1 \)) is positioned directly between these two planets.Given:- \( M_3 = 16 \, M_2 \)- \( R = 15 \)The task is to find the value of \( r \) such that the total gravitational force on Planet #1 is zero.\[ \text{r} = \_\_\_\_ \]

Using, Gravitational force, F=GMmr2 Net force on mass-1 F1,netis zero, that means, sum of gravitational forces by mass-2 F1,2 and mass-3 F1,3 is zero. F1,net=F1,2+F1,3=0F1,2=acts on mass-1 towards rightF1,3=acts on mass-1 towards leftGM1M2r2-GM3M1R-r2=0M1M2r2=M3M1R-r2 [Since, M3=16M2, R=15 ]M1M2r2=16M2M115-r215-r2=16r2r2+2r-15=0r+5r-3=0r=3 [r=-5 cannot be taken as r negative does not make sense here]Answer: r = 3

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Pl anet # 1 M3 M: M2 R R NI u ....I R Planet # 3 Planet # 2 Planet #2 (mass M2) and planet #3 (mass M3) are separated by distance R. Planet #1 (mass M1) is directly between these two planets. If M3 = 16 M2 and R=15, then what is the value of r such that the total force on planet #1 is zero?

Pl anet # 1 M3 M: M2 R R NI u ....I R Planet # 3 Planet # 2 Planet #2 (mass M2) and planet #3 (mass M3) are separated by distance R. Planet #1 (mass M1) is directly between these two planets. If M3 = 16 M2 and R=15, then what is the value of r such that the total force on planet #1 is zero?

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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