Let's determine the gravitational force between two laptop computers with a mass of [tex]\(2 \, \text{kg}\)[/tex] each, separated by a distance of [tex]\(0.5 \, \text{m}\)[/tex]. We will use the gravitational force formula:
[tex]\[
F = G \frac{m_1 \cdot m_2}{r^2}
\][/tex]
Where:
- [tex]\(F\)[/tex] is the gravitational force.
- [tex]\(G\)[/tex] is the gravitational constant, [tex]\(6.67 \times 10^{-11} \, \text{N} \cdot (\text{m}/\text{kg})^2\)[/tex].
- [tex]\(m_1\)[/tex] and [tex]\(m_2\)[/tex] are the masses of the two objects, each [tex]\(2 \, \text{kg}\)[/tex] in this case.
- [tex]\(r\)[/tex] is the distance between the two objects, [tex]\(0.5 \, \text{m}\)[/tex].
First, substitute the known values into the formula:
[tex]\[
F = (6.67 \times 10^{-11}) \frac{2 \times 2}{(0.5)^2}
\][/tex]
Calculate the denominator:
[tex]\[
(0.5)^2 = 0.25
\][/tex]
Now calculate the numerator:
[tex]\[
2 \times 2 = 4
\][/tex]
Next, compute the fraction:
[tex]\[
\frac{4}{0.25} = 16
\][/tex]
Finally, multiply by the gravitational constant:
[tex]\[
F = 6.67 \times 10^{-11} \times 16
\][/tex]
To find the final value:
[tex]\[
F = 1.0672 \times 10^{-9} \, \text{N}
\][/tex]
This means that the gravitational force between the two laptops is [tex]\(1.0672 \times 10^{-9} \, \text{N}\)[/tex].
Thus, the correct answer is:
D. [tex]\(1.07 \times 10^{-9} \, \text{N}\)[/tex]
