If The Distance Between Two Objects Is Increased By A Factor Of 3 (tripled), How Will This Affect $F_g$?A. $F_g$ Increases By 3 Times B. $F_g$ Decreases To $\frac{1}{3}$ C. $F_g$ Decreases To

Introduction

In the realm of physics, particularly in the study of gravity, the distance between two objects plays a crucial role in determining the gravitational force acting between them. The gravitational force, denoted by $F_g$, is a fundamental force of nature that attracts two objects with mass towards each other. In this article, we will explore how increasing the distance between two objects affects the gravitational force.

Gravitational Force and Distance

The gravitational force between two objects is given by the formula:

$$F_g = \frac{G \cdot m_1 \cdot m_2}{r^2}$$

where:

• $G$ 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

From this formula, we can see that the gravitational force is inversely proportional to the square of the distance between the objects. This means that as the distance between the objects increases, the gravitational force decreases.

Effect of Increasing Distance on Gravitational Force

Now, let's consider the scenario where the distance between two objects is increased by a factor of 3, i.e., tripled. We want to determine how this increase in distance affects the gravitational force.

If the distance is tripled, the new distance is $3r$. Substituting this value into the formula for gravitational force, we get:

$$F_g' = \frac{G \cdot m_1 \cdot m_2}{(3r)^2}$$

Simplifying this expression, we get:

$$F_g' = \frac{G \cdot m_1 \cdot m_2}{9r^2}$$

Comparing this expression with the original formula for gravitational force, we can see that the gravitational force has decreased by a factor of 9.

Conclusion

In conclusion, if the distance between two objects is increased by a factor of 3, the gravitational force decreases by a factor of 9. This is because the gravitational force is inversely proportional to the square of the distance between the objects.

Answer

The correct answer is:

C. $F_g$ decreases to $\frac{1}{9}$

Discussion

This result makes intuitive sense, as we would expect the gravitational force to decrease as the distance between the objects increases. However, the exact relationship between distance and gravitational force is more complex and depends on the specific formula used to describe the gravitational force.

Real-World Applications

Understanding the relationship between distance and gravitational force has important implications in various fields, such as:

• Astronomy: The gravitational force between celestial bodies, such as planets and stars, plays a crucial role in determining their orbits and motion.
• Space Exploration: The gravitational force between spacecraft and celestial bodies must be taken into account when planning space missions.
• Geophysics: The gravitational force between the Earth and other celestial bodies affects the Earth's tides and ocean currents.

Conclusion

Frequently Asked Questions About Gravitational Force

Q: What is the gravitational force?

A: The gravitational force, denoted by $F_g$, is a fundamental force of nature that attracts two objects with mass towards each other.

Q: What is the formula for gravitational force?

A: The formula for gravitational force is:

$$F_g = \frac{G \cdot m_1 \cdot m_2}{r^2}$$

where:

• $G$ 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

Q: Is the gravitational force always attractive?

A: Yes, the gravitational force is always attractive. It is a force that pulls two objects with mass towards each other.

Q: Can the gravitational force be repulsive?

A: No, the gravitational force is never repulsive. It is always attractive.

Q: How does the gravitational force change with distance?

A: The gravitational force decreases as the distance between the objects increases. This is because the gravitational force is inversely proportional to the square of the distance between the objects.

Q: What happens to the gravitational force if the distance is tripled?

A: If the distance is tripled, the gravitational force decreases by a factor of 9.

Q: Can the gravitational force be zero?

A: Yes, the gravitational force can be zero if the distance between the objects is infinite.

Q: What is the gravitational force between two objects of equal mass?

A: The gravitational force between two objects of equal mass is zero if the distance between them is infinite. However, if the distance is finite, the gravitational force is not zero.

Q: Can the gravitational force be negative?

A: No, the gravitational force is always positive. It is a force that attracts two objects with mass towards each other.

Q: What is the gravitational force between a planet and a satellite?

A: The gravitational force between a planet and a satellite is determined by the mass of the planet and the mass of the satellite, as well as the distance between them.

Q: Can the gravitational force be affected by other forces?

A: Yes, the gravitational force can be affected by other forces, such as the electromagnetic force and the strong and weak nuclear forces.

Q: What is the gravitational force between two objects in a vacuum?

A: The gravitational force between two objects in a vacuum is the same as the gravitational force between them in a non-vacuum environment.

Q: Can the gravitational force be measured directly?

A: No, the gravitational force cannot be measured directly. However, its effects can be measured and observed.

Q: What is the gravitational force between two objects on the surface of the Earth?

A: The gravitational force between two objects on the surface of the Earth is determined by the mass of the objects and the distance between them.

Conclusion

In conclusion, the gravitational force is a fundamental force of nature that attracts two objects with mass towards each other. Understanding the gravitational force is essential in various fields, including astronomy, space exploration, and geophysics.