Final answer:
To find the mass of each lead sphere, we can use the equation for gravitational force. Plugging in the given values and solving, we find that each sphere has a mass of 4.431 * 10^-4 kg.
Step-by-step explanation:
To find the mass of each lead sphere, we can use the equation for gravitational force: F = G * ((m1 * m2) / r^2), where F is the force, G is the gravitational constant, m1 and m2 are the masses of the spheres, and r is the distance between them.
In this case, the force between the spheres is 5.8 x 10^-8 N and the distance is 0.60 m.
Plugging in these values and solving for the masses:
F = G * ((m1 * m2) / r^2)
5.8 x 10^-8 N = (6.67430 x 10^-11 N(m^2/kg^2) * ((m1 * m2) / (0.60 m)^2)
Simplifying the equation:
5.8 x 10^-8 N = (6.67430 x 10^-11 N(m^2/kg^2) * ((m1 * m2) / 0.36 m^2)
5.8 x 10^-8 N * 0.36 m^2 = 6.67430 x 10^-11 N(m^2/kg^2) * (m1 * m2)
(5.8 x 10^-8 N * 0.36 m^2) / 6.67430 x 10^-11 N(m^2/kg^2) = m1 * m2
Plugging in the values and solving:
(5.8 x 0.36 * 10^-8 N * m^2) / (6.67430 x 10^-11 N(m^2/kg^2)) = m1 * m2
1.968 * 10^-8 = m1 * m2
Since the spheres are identical, m1 = m2.
So, m1 * m2 = m1^2.
1.968 * 10^-8 = m1^2
Taking the square root of both sides:
m1 = 4.431 * 10^-4 kg
Therefore, each sphere has a mass of 4.431 * 10^-4 kg.