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

Explanation

To find the gravitational force of attraction between two spherical balls, we can 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:
- \( F \) is the gravitational force,
- \( G \) is the universal gravitational constant, approximately \( 6.674 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \),
- \( m_1 \) 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 \( r = 10 \, \text{cm} = 0.1 \, \text{m} \) (convert cm to m)

2. **Substitute the values into the formula**:
\[ F = G \frac{m_1 m_2}{r^2} \]
Substituting the known values:
\[ F = (6.674 \times 10^{-11} \, \text{N m}^2/\text{kg}^2) \frac{(10 \, \text{kg}) (10 \, \text{kg})}{(0.1 \, \text{m})^2} \]

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

4. **Calculate the force**:
\[ F = (6.674 \times 10^{-11}) \frac{100}{0.01} \]
\[ F = (6.674 \times 10^{-11}) \times 10000 \]
\[ F = 6.674 \times 10^{-7} \, \text{N} \]

### Final Answer:
The gravitational force of attraction between the two spherical balls is approximately \( 6.674 \times 10^{-7} \, \text{N} \).

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