Final answer:
Using the principles of Newton's law of universal gravitation, the gravitational force between two bodies when they are 2m apart is calculated to be approximately 0.0123 N.
Step-by-step explanation:
The gravitational force between two bodies is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. According to Newton's law of universal gravitation, the formula to calculate the gravitational force F is:
F = G (m1*m2) / r²
where G is the gravitational constant (6.674 × 10⁻¹¹ N*m²/kg²), m1 and m2 are the masses of the two bodies, and r is the distance between the centers of the two bodies.
To calculate the new gravitational force when the distance between the bodies is 2 meters, using the proportionality of the forces with the change in distance, we have:
F₁ / F₂ = r₂² / r₁²
25 / F₂ = 2² / 90²
F₂ = 25 * (2² / 90²)
F₂ = 25 *(4 / 8100)
F₂ = 25 * (1 / 2025)
F₂ = 25 / 2025
F₂ = 0.0123 N (Approximately)