The gravitational force between two objects is 100 N. If the mass of each object is doubled.what is the gravitational force between the objects at the same distance? 25 N 50 N 200 N 400 N

## Step 1<br />The gravitational force between two objects is given by the formula:<br />### \(F = G \frac{m1 \cdot m2}{r^2}\)<br />where \(F\) is the gravitational force, \(G\) is the gravitational constant, \(m1\) and \(m2\) are the masses of the two objects, and \(r\) is the distance between the two objects.<br /><br />## Step 2<br />According to the problem, the mass of each object is doubled. This means that the new masses of the two objects are \(2m1\) and \(2m2\).<br /><br />## Step 3<br />Substitute the new masses into the formula to find the new gravitational force:<br />### \(F' = G \frac{2m1 \cdot 2m2}{r^2} = 4G \frac{m1 \cdot m2}{r^2} = 4F\)<br /><br />## Step 4<br />The original gravitational force \(F\) is given as 100 N. Therefore, the new gravitational force \(F'\) is 4 times the original force, which is \(4 \times 100 N = 400 N\).