Final answer:
The separation between the two particles must be 1.082 meters for their gravitational attraction to have a magnitude of 2.3 x 10^12 N.
Step-by-step explanation:
The magnitude of the gravitational force between two objects can be calculated using Newton's law of universal gravitation:
F = G * ((m1 * m2) / r^2)
Where F is the magnitude of the gravitational force, G is the gravitational constant (6.674 × 10^-11 N·m²/kg²), m1 and m2 are the masses of the objects, and r is the separation between them.
In this case, we have a particle with a mass of 5.2 kg and another particle with a mass of 2.4 kg. We are given that the magnitude of their gravitational attraction is 2.3 x 10^12 N. We can rearrange the formula to solve for r:
r = sqrt((G * (m1 * m2)) / F)
Plugging in the values, we get:
r = sqrt((6.674 × 10^-11 N·m²/kg² * (5.2 kg * 2.4 kg)) / (2.3 × 10^12 N))
r = 1.082 meters
Therefore, the separation between the two particles must be 1.082 meters for their gravitational attraction to have a magnitude of 2.3 x 10^12 N.