https://file.aiquickdraw.com/mathbot/file/1727373208694g1syjmzl.jpg

The problem is asking what happens to the gravitational force between two objects when the distance between them is doubled, given the initial force of 100 N.

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

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

Where:
- \( G \) is the gravitational constant,
- \( m_1 \) and \( m_2 \) are the masses of the objects,
- \( r \) is the distance between the objects.

If the distance \( r \) is doubled, the new gravitational force \( F' \) becomes:

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

So, when the distance is doubled, the force is reduced to one-quarter of its original value. Since the original force is 100 N, the new force would be:

\[
F' = \frac{100 \, \text{N}}{4} = 25 \, \text{N}
\]

Thus, the correct answer is **25 newtons**.

Would you like more details or have any questions? Here are five related questions for further exploration:

1. How would the gravitational force change if the distance was tripled?
2. What happens to the force if the masses of both objects are doubled?
3. How does the gravitational force between objects change if one of the objects' mass is halved?
4. What is the significance of the gravitational constant \( G \)?
5. How does gravitational force vary with altitude on Earth?

**Tip:** Gravitational force decreases rapidly with increasing distance because it follows an inverse-square law.

The gravitational force between two objects is 100 N. What would the gravitational force be if the distance between them were doubled?

Learn how to calculate the new gravitational force between two objects when the distance between them is doubled. This problem involves Newton's law of universal gravitation and demonstrates the inverse-square law. Suitable for high school physics students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation