To calculate the gravitational force of attraction between the two balls, we use Newton's law of universal gravitation. The formula for gravitational force [tex]\( F \)[/tex] is:
[tex]\[ F = G \frac{m_1 \cdot m_2}{r^2} \][/tex]
where:
- [tex]\( G \)[/tex] is the gravitational constant ([tex]\( 6.673 \times 10^{-11} \, \text{Nm}^2/\text{kg}^2 \)[/tex])
- [tex]\( m_1 \)[/tex] and [tex]\( m_2 \)[/tex] are the masses of the two balls (each 5 kg)
- [tex]\( r \)[/tex] is the distance between the centers of the two balls (0.33 m)
Step-by-step solution:
1. Substitute the known values into the formula:
[tex]\[ F = 6.673 \times 10^{-11} \, \text{Nm}^2/\text{kg}^2 \times \frac{5 \, \text{kg} \times 5 \, \text{kg}}{(0.33 \, \text{m})^2} \][/tex]
2. Calculate the product of the masses [tex]\( m_1 \)[/tex] and [tex]\( m_2 \)[/tex]:
[tex]\[ 5 \, \text{kg} \times 5 \, \text{kg} = 25 \, \text{kg}^2 \][/tex]
3. Calculate the square of the distance [tex]\( r \)[/tex]:
[tex]\[ (0.33 \, \text{m})^2 = 0.1089 \, \text{m}^2 \][/tex]
4. Substitute these values back into the formula:
[tex]\[ F = 6.673 \times 10^{-11} \times \frac{25}{0.1089} \][/tex]
5. Simplify the fraction:
[tex]\[ \frac{25}{0.1089} \approx 229.609 \][/tex]
6. Multiply the result by the gravitational constant:
[tex]\[ F \approx 6.673 \times 10^{-11} \times 229.609 \][/tex]
7. Perform the multiplication:
[tex]\[ F \approx 1.5319100091827363 \times 10^{-8} \][/tex]
Thus, the gravitational force of attraction between the two balls is approximately [tex]\( 1.5319100091827363 \times 10^{-8} \, \text{N} \)[/tex].
Therefore, the correct answer is:
[tex]\[ \boxed{1.5 \times 10^{-8} \, \text{N}} \][/tex]
So, the correct option is [tex]\( E \)[/tex].
