The force of gravitation between two bodies of mass 2 kg each separated by a distance of 2 m in vacuum is

Options

A. `6.67 xx 10^(-11) N`
B. `6.67 xx 10^(-10) N`
C. `6.67 xx 10^(-9)N`
D. none of these

Answer

To find the force of gravitation between two bodies of mass 2 kg each separated by a distance of 2 m in a vacuum, we can use Newton's law of universal gravitation. The formula for gravitational force (F) is given by:

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

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

### Step-by-Step Solution:

1. **Identify the values**:
- Mass of the first body, \( m_1 = 2 \, \text{kg} \)
- Mass of the second body, \( m_2 = 2 \, \text{kg} \)
- Distance between the two bodies, \( r = 2 \, \text{m} \)

2. **Substitute the values into the formula**:
\[ F = \frac{G \cdot m_1 \cdot m_2}{r^2} \]
\[ F = \frac{(6.67 \times 10^{-11}) \cdot (2) \cdot (2)}{(2)^2} \]

3. **Calculate \( r^2 \)**:
\[ r^2 = 2^2 = 4 \]

4. **Substitute \( r^2 \) back into the equation**:
\[ F = \frac{(6.67 \times 10^{-11}) \cdot 4}{4} \]

5. **Simplify the equation**:
\[ F = 6.67 \times 10^{-11} \, \text{N} \]

6. **Final Result**:
The gravitational force between the two bodies is:
\[ F = 6.67 \times 10^{-11} \, \text{N} \]