The gravitational force between two stones of mass 1 kg each separated by a distance of 1 metre in vacuum is

Options

A. Zero
B. `6 . 675 xx 10^(-1)` newton
C. `6 . 675 xx 10^(-11)` newton
D. `6 . 675 xx 10^(-8)` newton

Explanation

To find the gravitational force between two stones of mass 1 kg each, separated by a distance of 1 meter 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:
- \( F \) is the gravitational force,
- \( G \) is the 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 \( m_1 = 1 \, \text{kg} \)
- Given \( m_2 = 1 \, \text{kg} \)
- Given \( r = 1 \, \text{m} \)

2. **Substitute the values into the formula**:
\[ F = \frac{G \cdot m_1 \cdot m_2}{r^2} \]
\[ F = \frac{(6.674 \times 10^{-11} \, \text{N m}^2/\text{kg}^2) \cdot (1 \, \text{kg}) \cdot (1 \, \text{kg})}{(1 \, \text{m})^2} \]

3. **Calculate the denominator**:
\[ r^2 = (1 \, \text{m})^2 = 1 \, \text{m}^2 \]

4. **Calculate the gravitational force**:
\[ F = \frac{6.674 \times 10^{-11} \, \text{N m}^2/\text{kg}^2}{1 \, \text{m}^2} \]
\[ F = 6.674 \times 10^{-11} \, \text{N} \]

Thus, the gravitational force between the two stones is \( 6.674 \times 10^{-11} \, \text{N} \).

### Final Answer:
The gravitational force between the two stones is \( 6.674 \times 10^{-11} \, \text{N} \).