Two balls, each with a mass of 0.803 kg,

exert a gravitational force of 8.27 × 10
−11
N
on each other.
How far apart are the balls? The value
of the universal gravitational constant is
6.673 × 10
−11
N m2
/kg
2
.
Answer in units of

meters (m).

To find the distance between the two balls, we can use the equation for the gravitational force between two objects:

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

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

Rearranging the equation to solve for r, we have:

r = sqrt((G * m1 * m2) / F)

Plugging in the given values:
m1 = m2 = 0.803 kg
F = 8.27 × 10^-11 N
G = 6.673 × 10^-11 N m^2/kg^2

We can substitute these values into the equation to find the distance between the balls:

r = sqrt((6.673 × 10^-11 N m^2/kg^2 * 0.803 kg * 0.803 kg) / (8.27 × 10^-11 N))

Simplifying the expression:

r = sqrt(3.217 x 10^-21 m^3/kg^2) / (8.27 x 10^-11 N))

Taking the square root of the numerator and dividing by the denominator:

r = sqrt(3.217 x 10^-21) / 8.27 × 10^-11

Using a calculator:

r ≈ 7.02 × 10^-6 m

Therefore, the distance between the two balls is approximately 7.02 × 10^-6 meters (m).