Answer:
Approximately [tex]5.3\times 10^{-8}\; {\rm N}[/tex].
Explanation:
Look up the gravitational constant: [tex]G \approx 6.6743 \times 10^{-11}\; {\rm m^{3}\, kg^{-1}\, s^{-2}[/tex].
When two point masses [tex]M[/tex] and [tex]m[/tex] are separated with a distance of [tex]r[/tex], the gravitational force between the two point masses would be:
[tex]F = (G\, M\, m) / (r^{2})[/tex].
In this question, the masses are [tex]M = 10\; {\rm kg}[/tex] and [tex]m = 20\; {\rm kg}[/tex]. The distance between them is [tex]r = 0.5\; {\rm m}[/tex]. Assuming that the volume of the masses are negligible, the gravitational force between the masses would be:
[tex]\begin{aligned} &\frac{G\, M\, m}{r^{2}} \\ &= \frac{(6.6743 \times 10^{-11}\; {\rm m^{3}\, kg^{-1}\, s^{-2}})\, (10\; {\rm kg})\, (20\; {\rm kg})}{(0.5\; {\rm m})^{2}} \\ &\approx 5.3\; {\rm kg \cdot m\cdot s^{-2} \\ &= 5.3\; {\rm N}\end{aligned}[/tex].