Answered: Suppose two spheres fashioned of pure…

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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#20 Contigous Golden Spheres
Suppose two spheres fashioned of pure Gold are in contact. What must the radius of the spheres be such that the gravitational force among them is exactly 1.00 Newtons of force? Recall that the density of Gold is ρAU = 19, 300 kg/m^3, while the magnitude of the gravita- tional force among the spheres is given by the Universal Law of Gravitation:

Fg =G*(M1*M2)/ d2

where d is the distance between the geometric centers of the gold spheres. It may also help to note that the volume of a sphere is (4π /3)*R^3 .

A. 2.28 m B. 1.74 m C. 1.01 m D. 0.58 m

Expert Solution

Step 1 Formula

Formula of gravitational force between two identical sphere is as follows;

$F = \frac{G m^{2}}{r^{2}} 1)$

Where,

$m = M a s s r = R a d i u s o f a n o b j e c t G = u n i v e r s a l G r a v i t a t i o n a l c o n s \tan t$

$m = ρ V w h e r e, V = v o l u m e ρ = D e n s i t y$

$F = \frac{G ρ^{2} {(\frac{4}{3} {πr}^{3})}^{2}}{d^{2}} 2)$

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