3. Two masses, m1 and m2, are separated by a distance d. If the distance is quadrupled the gravitational force will: Use / Show Rule of One

## Step 1<br />The problem involves the concept of gravitational force, which is governed by Newton's law of universal gravitation. According to this law, the gravitational force between two masses is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. This relationship is mathematically represented as:<br />### \(F = G \frac{m1 \cdot m2}{d^2}\)<br />where \(F\) is the gravitational force, \(G\) is the gravitational constant, \(m1\) and \(m2\) are the masses, and \(d\) is the distance between the masses.<br /><br />## Step 2<br />The problem states that the distance between the two masses is quadrupled. This means that the new distance \(d'\) is \(4d\).<br /><br />## Step 3<br />Substitute \(d'\) into the formula for gravitational force to find the new force \(F'\).<br />### \(F' = G \frac{m1 \cdot m2}{(4d)^2}\)<br /><br />## Step 4<br />Simplify the equation to find the relationship between \(F'\) and \(F\).<br />### \(F' = G \frac{m1 \cdot m2}{16d^2}\)<br /><br />## Step 5<br />Comparing the original force \(F\) with the new force \(F'\), we can see that \(F'\) is \(\frac{1}{16}\) of \(F\). This means that when the distance is quadrupled, the gravitational force is reduced to \(\frac{1}{16}\) of its original value.