To find the gravitational force between the two cars, we use Newton's law of gravitation. The formula is given by:
[tex]\[ F_{\text{gravity}} = \frac{G m_1 m_2}{r^2} \][/tex]
where:
- [tex]\( G \)[/tex] is the gravitational constant, [tex]\( 6.67 \times 10^{-11} \, \text{N} \cdot \text{m}^2 / \text{kg}^2 \)[/tex]
- [tex]\( m_1 \)[/tex] is the mass of the first car, [tex]\( 2565 \, \text{kg} \)[/tex]
- [tex]\( m_2 \)[/tex] is the mass of the second car, [tex]\( 4264 \, \text{kg} \)[/tex]
- [tex]\( r \)[/tex] is the distance between the cars, [tex]\( 5 \, \text{m} \)[/tex]
Plugging these values into the formula, we get:
[tex]\[ F_{\text{gravity}} = \frac{(6.67 \times 10^{-11}) \times 2565 \times 4264}{5^2} \][/tex]
First, calculate the denominator:
[tex]\[ 5^2 = 25 \][/tex]
Next, compute the numerator:
[tex]\[ (6.67 \times 10^{-11}) \times 2565 \times 4264 \][/tex]
Combining the two results:
[tex]\[ F_{\text{gravity}} = \frac{(6.67 \times 10^{-11}) \times 2565 \times 4264}{25} \][/tex]
The result of this computation is:
[tex]\[ F_{\text{gravity}} = 2.92 \times 10^{-5} \, \text{N} \][/tex]
Therefore, the gravitational force between the two cars is [tex]\( 2.92 \times 10^{-5} \)[/tex] Newtons.
The correct answer is:
B. [tex]\( 2.92 \times 10^{-5} \, \text{N} \)[/tex]
