Question

Gravitational attraction depends on the mass of the objects as well as their distance. The gravitational force between objects increases as the masses of the objects increase. The gravitational force decreases as the distance between objects increases. The impact of mass and distance are not equal. If the mass of one object doubles, the gravitational force also doubles. If the distance between objects doubles, the gravitational force decreases by 1/4. Using the model predict what will happen to the gravitational force if the masses both double and the distance also doubles.

Answer 1

C) The gravitational attraction remains constant.

even though the distance is double The gravitational attraction remains constant no matter what.

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Answer 2

Answer: Gravitational attraction will be the same

According to the law of universal gravitation, which is a classical physical law that describes the gravitational interaction between different bodies with mass:

`F=G(m_(1)m_(2))/(r^2)` (1)

Where:

`F` is the module of the force exerted between both bodies

`G` is the universal gravitation constant.

`m_(1)` and
`m_(2)` are the masses of both bodies.

`r` is the distance between both bodies

Now, if we double both masses and the distance also doubles, this means:

`m_(1)` and
`m_(2)` will be now
`2m_(1)` and
`2m_(2)`

`r` will be now
`2r`

Let's rewrite the equation (1) with this new values:

`F=G((2m_(1))(2m_(2)))/((2r)^2)` (2)

Solving and simplifying:

`F=4G(m_(1)2m_(2))/(4r^2)`

`F=G(m_(1)m_(2))/(r^2)` (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.