To solve for \( r \) in the equation \( F = k \frac{Mm}{r^2} \), follow these steps:

1. **Start with the given equation:**
   \[
   F = k \frac{Mm}{r^2}
   \]

2. **Multiply both sides by \( r^2 \) to eliminate the fraction:**
   \[
   F \cdot r^2 = k \cdot Mm
   \]

3. **Divide both sides by \( F \) to isolate \( r^2 \):**
   \[
   r^2 = \frac{k \cdot Mm}{F}
   \]

4. **Take the square root of both sides to solve for \( r \):**
   \[
   r = \sqrt{\frac{k \cdot Mm}{F}}
   \]

So, the solution is:
\[
r = \sqrt{\frac{k \cdot Mm}{F}}
\]

Would you like more details or have any questions?

Here are five related questions to deepen your understanding:
1. How would the value of \( r \) change if the force \( F \) were doubled?
2. What happens to \( r \) if the constant \( k \) is increased?
3. How does the mass \( M \) affect the value of \( r \)?
4. Can you express \( r \) in terms of a different variable, such as \( F \), and explain its physical meaning?
5. What physical law or principle might this equation represent?

**Tip:** When manipulating equations with variables and constants, be careful to maintain the integrity of both sides of the equation. This ensures accurate results.

Discover how to solve for the radius (r) in the inverse square law equation F = k(Mm/r^2). This problem involves key algebraic and physical concepts, including the manipulation of variables and the inverse square law. Ideal for students in Grades 10-12.

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