Two spheres are placed at a distance of 10 m from each other. The force of gravity between them is 6.673x10 to the (-9)N. If one of the spheres is 4 times as massive as the other what are their masses in Kg?

the gravitational constant G =6.67•10⁻¹¹ N•m²/kg²,

F=6.673•10⁻⁹ N
R=10 m
F =G•m₁•m₂/R²= G•4m•m/R²= G•4m²/R²
m=sqrt{F R²/4G)=…

To find the masses of the spheres, we can use the equation for gravitational force:

F = (G * m1 * m2) / r^2

Where:
F is the gravitational force between the two spheres,
G is the gravitational constant (6.673 × 10^(-11) N m^2 / kg^2),
m1 and m2 are the masses of the two spheres, and
r is the distance between the centers of the two spheres.

Given that the distance (r) between the spheres is 10 m and the gravitational constant (G) is 6.673 × 10^(-11) N m^2 / kg^2, we can calculate the masses.

Let the mass of one sphere be "m" kg. Since the other sphere is 4 times as massive, its mass will be 4m kg.

Plugging the given values into the formula, we have:

6.673 × 10^(-11) N m^2 / kg^2 = (6.673 × 10^(-11) N m^2 / kg^2) * (m kg) * (4m kg) / (10 m)^2

Simplifying,

1 = (4m^2 * (6.673 × 10^(-11) N m^2 / kg^2)) / 100

Now, we can solve for "m":

100 = 4m^2 * (G)
m^2 = 100 / (4 * G)
m^2 = 100 / (4 * 6.673 × 10^(-11) N m^2 / kg^2)
m^2 ≈ 3 × 10^10 kg

Finding the square root of m^2:

m ≈ √(3 × 10^10 kg)
m ≈ 5.48 × 10^5 kg

Therefore, the mass of one sphere is approximately 5.48 × 10^5 kg, and the mass of the other sphere is approximately 4 times that mass, which is 4 * 5.48 × 10^5 kg = 2.19 × 10^6 kg.