Answer:
To find the mass of each object, we can use the formula for gravitational force:
F = (G * m1 * m2) / r²
Where:
F = gravitational force
G = gravitational constant (6.674 × 10^-11 N m²/kg²)
m1, m2 = masses of the objects
r = distance between the objects
Given:
F = 2.30 x 10^-8 N
r = 10.0 m
We can rearrange the formula to solve for the masses:
m1 * m2 = (F * r²) / G
Plugging in the given values:
m1 * m2 = (2.30 x 10^-8 N * (10.0 m)^2) / (6.674 × 10^-11 N m^2/kg^2)
m1 * m2 = (2.30 x 10^-8 N * 100 m^2) / (6.674 × 10^-11 N m^2/kg^2)
m1 * m2 = 2.30 x 10^-6 kg
Since both objects have equal mass, we can write m1 = m2 = m:
m^2 = 2.30 x 10^-6 kg
Taking the square root of both sides gives us:
m ≈ √(2.30 x 10^-6 kg)
m ≈ 0.00152 kg
So, the mass of each object is approximately 0.00152 kg.
