The gravitational force between two object is 100N. How should the distance between these object be changed so that force between them becomes 50N.

Explanation

To solve the problem, we will use Newton's Law of Universal Gravitation, which states that the gravitational force \( F \) between two masses \( m_1 \) and \( m_2 \) separated by a distance \( r \) is given by the formula:

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

where \( G \) is the gravitational constant.

### Step-by-Step Solution:

1. **Identify Initial Conditions:**
- The initial gravitational force \( F_1 = 100 \, \text{N} \).
- Let the initial distance between the two objects be \( r \).

2. **Set Up the Equation for Initial Force:**
\[ F_1 = G \frac{m_1 m_2}{r^2} \]
This means:
\[ 100 = G \frac{m_1 m_2}{r^2} \quad (1) \]

3. **Identify Final Conditions:**
- The final gravitational force \( F_2 = 50 \, \text{N} \).
- Let the new distance be \( r' \).

4. **Set Up the Equation for Final Force:**
\[ F_2 = G \frac{m_1 m_2}{(r')^2} \]
This means:
\[ 50 = G \frac{m_1 m_2}{(r')^2} \quad (2) \]

5. **Divide the Two Equations:**
To find the relationship between \( r \) and \( r' \), divide equation (1) by equation (2):
\[ \frac{100}{50} = \frac{G \frac{m_1 m_2}{r^2}}{G \frac{m_1 m_2}{(r')^2}} \]
Simplifying this gives:
\[ 2 = \frac{(r')^2}{r^2} \]

6. **Rearranging the Equation:**
\[ \frac{(r')^2}{r^2} = 2 \]
Taking the square root of both sides:
\[ \frac{r'}{r} = \sqrt{2} \]

7. **Finding the New Distance:**
Thus, we can express \( r' \) in terms of \( r \):
\[ r' = r \sqrt{2} \]

### Conclusion:
To reduce the gravitational force from 100 N to 50 N, the distance between the two objects should be increased to \( r \sqrt{2} \).