Question

Objects 1 and 2 attract each other with a gravitational force
of 36.0 units. If the distance separating Objects 1 and 2 is
doubled, then the new gravitational force will be
units.

Answer 1

The new gravitational force will be 9 units

Explanation:

The magnitude of the gravitational force between two objects is given by

$F=\frac{Gm_1 m_2}{r^2}$

where

G is the gravitational constant

$m_1, m_2$ are the masses of the two objects

r is the distance separating the two objects

Let's call

F = 36 units

the initial gravitational force between the two objects here, when they are separated by a distance r.

Later, the distance is doubled, so

r' = 2r

So the new force is

$F'=\frac{Gm_1 m_2}{r'^2}=\frac{Gm_1 m_2}{(2r)^2}=\frac{1}{4} (\frac{Gm_1 m_2}{r^2})=\frac{1}{4}F$

So, the gravitational force has decreased by a factor 4, and therefore the new value is

$F'=\frac{36}{4}=9$ units

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