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We are tasked with calculating the gravitational force between two spherical objects using Newton's law of universal gravitation. The formula for the gravitational attraction \( F \) is:

\[
F = \frac{G \cdot m_1 \cdot m_2}{r^2}
\]

Where:
- \( G = 6.67 \times 10^{-11} \, \text{N} \cdot \text{m}^2 / \text{kg}^2 \) (gravitational constant),
- \( m_1 = 200 \, \text{kg} \),
- \( m_2 = 500 \, \text{kg} \),
- \( r = 25 \, \text{m} \) (distance between their centers).

Let's plug in the values:

\[
F = \frac{(6.67 \times 10^{-11}) \cdot (200) \cdot (500)}{25^2}
\]

First, calculate the denominator:
\[
25^2 = 625
\]

Now calculate the numerator:
\[
6.67 \times 10^{-11} \times 200 \times 500 = 6.67 \times 10^{-11} \times 100000 = 6.67 \times 10^{-6}
\]

Now divide the numerator by the denominator:
\[
F = \frac{6.67 \times 10^{-6}}{625} = 1.0672 \times 10^{-8} \, \text{N}
\]

This result is approximately \( 1.1 \times 10^{-8} \, \text{N} \).

So, the correct answer is **A. \( 1.1 \times 10^{-8} \, \text{N} \)**.

Would you like more details on this calculation or a different explanation?

Here are 5 related questions to deepen your understanding:
1. How does the gravitational force change if the distance between the objects doubles?
2. What would happen to the force if one of the masses is halved?
3. How would the force differ on a larger scale, like between celestial bodies?
4. What role does the gravitational constant \( G \) play in this calculation?
5. How does Newton's law of gravitation compare with Einstein's theory of general relativity?

**Tip:** Gravitational force decreases with the square of the distance, meaning even a small increase in distance can significantly reduce the force.

Two spherical objects have masses of 200 kg and 500 kg. Their centers are separated by a distance of 25 m. G = 6.67 x 10^-11 N·m²/kg². Find the gravitational attraction between them.

Learn how to calculate the gravitational force between two objects with masses of 200 kg and 500 kg, separated by 25 m. Using Newton's law of universal gravitation and the formula F = (G * m1 * m2) / r^2, this problem illustrates key physics concepts. Suitable for high school students.

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