Question

The gravitational force between two objects is 1600 N. What will be the gravitational force between the objects if the distance between them doubles?

400 N
800 N
3200 N
6400 N

Answer 1

The gravitational force between two objects is given by Newton's law of universal gravity:

\[
F = \frac{G \cdot m_1 \cdot m_2}{r^2}
\]

where:
- \(F\) is the gravitational force,
- \(G\) is the gravitational constant,
- \(m_1\) and \(m_2\) are the masses of the two objects,
- \(r\) is the distance between the centers of the two objects.

If the distance \(r\) between the two objects doubles, the new distance becomes \(2r\). The new gravitational force \(F'\) can be expressed as:

\[
F' = \frac{G \cdot m_1 \cdot m_2}{(2r)^2} = \frac{G \cdot m_1 \cdot m_2}{4r^2} = \frac{F}{4}
\]

Since the original force \(F\) is 1600 N, the new force will be:

\[
F' = \frac{1600 \, \text{N}}{4} = 400 \, \text{N}
\]

Therefore, the gravitational force between the objects if the distance between them doubles will be **400 N**.