Final answer:
Using Newton's Law of Universal Gravitation, the gravitational force between two 5-kg masses separated by 15 cm is calculated to be approximately 1.48 \(\times\) 10^-9 N, which does not match any of the provided options, indicating a possible error in the question or options.
Step-by-step explanation:
The problem posed falls under the domain of Physics and involves utilizing Newton's Law of Universal Gravitation to determine the gravitational force between two objects. Specifically, to calculate the force between two 5-kg spherical steel balls separated by a center-to-center distance of 0.15 m (15 cm).
The formula for this calculation is:
F = G \(\frac{m1 \cdot m2}{r^2}\)
Where:
Plugging the given values into the formula, we get:
F = (6.674 \(\times\) 10^-11 Nm^2/kg^2) \(\frac{(5 kg) \cdot (5 kg)}{(0.15 m)^2}\) = 6.674 \(\times\) 10^-11 \(\times\) \(\frac{25}{0.0225}\)
After performing the calculations, we get:
F \(\approx\) 1.48 \(\times\) 10^-9 N
However, since this value is not one of the provided options, we must conclude that a typographical error has occurred in the problem statement or the provided options.