Question

Two uniform spheres, each with mass M and radius R , touch one another.


Part A
What is the magnitude of their gravitational force of attraction?
Express your answer in terms of the variables M, R , and appropriate constants.

Answer 1

Two uniform spheres, each with mass M and radius R ,touch one another.
What is the magnitude of their gravitationalforce of attraction?
wouldnt that just be F=G* M2/(R+R)2 ?

mass of each sphere =[4/3]*pR3*density
now the gravitational force of attraction=GM*M/(2R)2
substituting the values we get
F=G*{[4/3]*pR3*density}2/4R2
simplifying we getF=4/9*p2R4(density)2G

Answer 2

The answer is GM^2 / 4R^2 - this comes from the fact that their separation distance is simply twice their radius (since they have the same radius) and their masses are the same. Plugging all of these into the Universal Gravitation equation, GMm/R^2, you get GMM/(2R)^2 which simplifies to GM^2 / 4R^2. Hope this helps!

Answer 3

The answer is GM^2 / 4R^2 - this comes from the fact that their separation distance is simply twice their radius (since they have the same radius) and their masses are the same. Plugging all of these into the Universal Gravitation equation, GMm/R^2, you get GMM/(2R)^2 which simplifies to GM^2 / 4R^2. Hope this helps!