### Problem Statement**4.** Two point masses \( m \) and \( 10m \) lie along the x-axis, with \( m \) at the origin and \( 10m \) at \( x = L \). A third point mass \( M \) is moved along the x-axis.**(a)** At what point is the net gravitational force on \( M \) due to the other two masses equal to zero?**(b)** Sketch the x-component of the net force on \( M \) due to \( m \) and \( 10m \), taking quantities to the right as positive. Include the regions \( x < 0 \); \( 0 < x < L \), and \( x > L \). Be especially careful to show the behavior of the graph on either side of \( x = 0 \) and \( x = L \).---### Explanation and SolutionThe problem involves understanding the gravitational forces between three masses aligned on the x-axis and determining where the forces balance each other out.#### Part (a) - Equilibrium PointTo find the point where the net gravitational force on \( M \) due to \( m \) and \( 10m \) is zero:1. **Gravitational Force** - The gravitational force \( F \) between two masses \( m_1 \) and \( m_2 \) separated by a distance \( r \) is given by: \[ F = G \frac{m_1 m_2}{r^2} \] where \( G \) is the gravitational constant.2. **Setup the Forces** - Let the distance from \( m \) at the origin to \( M \) be \( x \). - The distance from \( 10m \) at \( x = L \) to \( M \) is \( L - x \).3. **Equating Forces** - The force on \( M \) due to \( m \) at the origin is: \[ F_{m \to M} = G \frac{m M}{x^2} \] - The force on \( M \) due to \( 10m \) at \( x = L \) is: \[ F_{10m \to M} = G \frac{10m M}{(L - x

Name: ### Problem Statement**4.** Two point masses \( m \) and \( 10m \) l
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Description: ### Problem Statement**4.** Two point masses \( m \) and \( 10m \) lie along the x-axis, with \( m \) at the origin and \( 10m \) at \( x = L \). A third point mass \( M \) is moved along the x-axis.**(a)** At what point is the net gravitational fo

Let M be at r units from m so that it will be (L-r) from 10m. Then, the gravitational force between…

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[4.] Two point masses m and 10 m lie along the x-axis, with m at the origin and 10 m at x = L. A third point mass M is moved along the x-axis. (a) At what point is the net gravitational force on M due to the other two masses equal to zero? (b) Sketch the x-component of the net force on M due to m and 10m taking quantities to the right as positive. Include the regions x < 0; 0 < x < L, and x > L. Be especially careful to show the behavior of the graph on either side of x = 0 and x = L.

[4.] Two point masses m and 10 m lie along the x-axis, with m at the origin and 10 m at x = L. A third point mass M is moved along the x-axis. (a) At what point is the net gravitational force on M due to the other two masses equal to zero? (b) Sketch the x-component of the net force on M due to m and 10m taking quantities to the right as positive. Include the regions x < 0; 0 < x < L, and x > L. Be especially careful to show the behavior of the graph on either side of x = 0 and x = L.

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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