To determine the distance between the two tables given their masses and the gravitational force between them, we will use the formula for gravitational force:
[tex]\[ F = G \times \frac{m1 \times m2}{d^2} \][/tex]
Where:
- [tex]\( F \)[/tex] is the gravitational force between the two objects,
- [tex]\( G \)[/tex] is the gravitational constant,
- [tex]\( m1 \)[/tex] and [tex]\( m2 \)[/tex] are the masses of the two objects,
- [tex]\( d \)[/tex] is the distance between the centers of the two masses.
First, let's rearrange the formula to solve for the distance [tex]\( d \)[/tex]:
[tex]\[ d^2 = G \times \frac{m1 \times m2}{F} \][/tex]
Taking the square root of both sides gives us:
[tex]\[ d = \sqrt{G \times \frac{m1 \times m2}{F}} \][/tex]
Now, let's plug in the given values:
- [tex]\( m1 = 29 \, \text{kg} \)[/tex]
- [tex]\( m2 = 29 \, \text{kg} \)[/tex]
- [tex]\( F = 4.24 \times 10^{-10} \, \text{N} \)[/tex]
- [tex]\( G = 6.67 \times 10^{-11} \, \text{N} \cdot (\text{m} / \text{kg})^2 \)[/tex]
Substituting these values into the equation:
[tex]\[ d = \sqrt{(6.67 \times 10^{-11}) \times \frac{(29)(29)}{4.24 \times 10^{-10}}} \][/tex]
Upon performing the calculation, we find:
[tex]\[ d \approx 11.502122445649627 \, \text{m} \][/tex]
Thus, the distance between the two tables is approximately 11.5 meters. Therefore, the correct answer is:
B. [tex]\( 11.5 \, \text{m} \)[/tex]
