According to the law of universal gravitation, which is a classical physical law that describes the gravitational interaction between different bodies with mass:
[tex]F=G\frac{m_{1}m_{2}}{r^2}[/tex] (1)
Where:
[tex]F[/tex] is the module of the force exerted between both bodies
[tex]G[/tex] is the universal gravitation constant.
[tex]m_{1}[/tex] and [tex]m_{2}[/tex] are the masses of both bodies.
[tex]r[/tex] is the distance between both bodies
Now, if we double both masses and the distance also doubles, this means:
[tex]m_{1}[/tex] and [tex]m_{2}[/tex] will be now [tex]2m_{1}[/tex] and [tex]2m_{2}[/tex]
[tex]r[/tex] will be now [tex]2r[/tex]
Let's rewrite the equation (1) with this new values:
[tex]F=G\frac{(2m_{1})(2m_{2})}{(2r)^2}[/tex] (2)
Solving and simplifying:
[tex]F=4G\frac{m_{1}2m_{2}}{4r^2}[/tex]
[tex]F=G\frac{m_{1}m_{2}}{r^2}[/tex] (3)
As we can see, equation (3) is the same as equation (1).
So, if the masses both double and the distance also doubles the Gravitational attraction between both masses will remain the same.
Answer:
C) The gravitational attraction remains constant.
even though the distance is double The gravitational attraction remains constant no matter what.
I hope this helps!!!
Your welcome,
Shadow Lolbit
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