If the gravitational force between two objects with masses of 6 kg and 12 kg is 48 N, what would the gravitational force be if the mass of the first object is increased to 12 kg while the second object remains the same?

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

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

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.

Now, in your problem, the initial gravitational force \( F_1 \) between masses \( m_1 = 6 \, \text{kg} \) and \( m_2 = 12 \, \text{kg} \) is given as \( 48 \, \text{N} \). Thus:

\[
F_1 = G \frac{(6)(12)}{r^2} = 48 \, \text{N}
\]

Next, the mass of the first object is increased to \( 12 \, \text{kg} \) while the second mass remains \( 12 \, \text{kg} \). The new gravitational force \( F_2 \) is then:

\[
F_2 = G \frac{(12)(12)}{r^2}
\]

To find the relationship between \( F_2 \) and \( F_1 \), we divide \( F_2 \) by \( F_1 \):

\[
\frac{F_2}{F_1} = \frac{G \frac{(12)(12)}{r^2}}{G \frac{(6)(12)}{r^2}} = \frac{12}{6} = 2
\]

Thus, \( F_2 = 2 \times F_1 = 2 \times 48 = 96 \, \text{N} \).

### Conclusion:
The gravitational force would increase to \( 96 \, \text{N} \) when the mass of the first object is increased to \( 12 \, \text{kg} \), while the second object remains the same.

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### Relative Questions:
1. How does distance between the objects affect gravitational force?
2. What happens to the gravitational force if both masses are doubled?
3. Can gravitational force ever be negative?
4. How would the force change if the distance between the objects is halved?
5. How does gravitational force compare to other fundamental forces?

### Tip:
The gravitational force is directly proportional to the product of the two masses, so doubling one mass doubles the force.

Explore how the gravitational force changes when the mass of one object is doubled. This detailed example covers Newton's law of universal gravitation, showing how increasing the mass of one object from 6 kg to 12 kg affects the force between it and a 12 kg object. Suitable for high school students studying physics.

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