Question

Anylayze this chart on the effect of Mass on Gravitational Force between two objects:

Question: What happens to the Gravitational Force if ONE of the object's Mass was CUT IN HALF, while the other remained the same?









a
The gravitational force is halved
b
The gravitational force is doubled
c
The gravitational force is quadrupled
d
The gravitational force is cut into one fourth

Answer 1

The gravitational force \( F \) between two objects is described by Newton's law of universal gravitation, which states:

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

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 we cut the mass of one of the objects (say \( m_1 \)) in half, the new mass \( m_1' \) will be:

\[
m_1' = \frac{m_1}{2}
\]

Assuming the other mass \( m_2 \) and the distance \( r \) remain constant, the new gravitational force \( F' \) can be expressed as:

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

Simplifying this, we have:

\[
F' = \frac{1}{2} \left(G \frac{m_1 m_2}{r^2}\right) = \frac{1}{2} F
\]

This shows that if one of the object's masses is cut in half, the gravitational force between the two objects is also cut in half.

Therefore, the correct answer is:

**a. The gravitational force is halved.**