Two spherical balls of mass 10 kg each are placed 10 cm apart. Find the gravitational force of attraction between them.

Explanation

To find the gravitational force of attraction between two spherical balls of mass 10 kg each placed 10 cm apart, we can use Newton's law of universal gravitation, which states:

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

Where:
- \( F \) is the gravitational force,
- \( G \) is the gravitational constant (\( 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \)),
- \( m_1 \) and \( m_2 \) are the masses of the two objects,
- \( r \) is the distance between the centers of the two masses.

### Step-by-Step Solution:

1. **Identify the masses and distance**:
- Given: \( m_1 = 10 \, \text{kg} \)
- Given: \( m_2 = 10 \, \text{kg} \)
- Given distance \( r = 10 \, \text{cm} \)

2. **Convert the distance from centimeters to meters**:
- Since \( 1 \, \text{cm} = 0.01 \, \text{m} \), we convert:
\[ r = 10 \, \text{cm} = 10 \times 0.01 \, \text{m} = 0.1 \, \text{m} \]

3. **Substitute the values into the gravitational force formula**:
\[ F = \frac{G \cdot m_1 \cdot m_2}{r^2} \]
Substituting the known values:
\[ F = \frac{6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \cdot 10 \, \text{kg} \cdot 10 \, \text{kg}}{(0.1 \, \text{m})^2} \]

4. **Calculate \( r^2 \)**:
\[ r^2 = (0.1 \, \text{m})^2 = 0.01 \, \text{m}^2 \]

5. **Plug \( r^2 \) back into the equation**:
\[ F = \frac{6.67 \times 10^{-11} \cdot 10 \cdot 10}{0.01} \]

6. **Calculate the numerator**:
\[ 10 \cdot 10 = 100 \]
Therefore,
\[ F = \frac{6.67 \times 10^{-11} \cdot 100}{0.01} \]

7. **Simplify the expression**:
\[ F = \frac{6.67 \times 10^{-9}}{0.01} = 6.67 \times 10^{-9} \cdot 100 = 6.67 \times 10^{-7} \, \text{N} \]

8. **Final Result**:
\[ F = 6.67 \times 10^{-7} \, \text{N} \]

### Conclusion:
The gravitational force of attraction between the two spherical balls is \( 6.67 \times 10^{-7} \, \text{N} \).