Q1: Find the electric charge required on the earth and moon to balance their gravitational attraction if the charge on the earth is 12.5 times that on the moon.
Mass of moon = 6.7 x 10²² Kg
Mass of earth = 6 x 10²⁴ Kg
Distance between moon and earth = 380 Km
Universal gravitational constant = 6.7 x 10^-11 Nm²/Kg²

Using law of gravitations, the force between two point masses is F = M₁ = mass of moon = 6.7 x 10²² kg M₂ = mass of earth = 6 x 10²⁴ kg r = distance between masses = 380 km G = universal gravitational constant = 6.7 x 10^{- 11} Nm²/Kg² Let Q₁ and Q₂ be the charge on moon and earth respectively. Now the gravitational force must be balanced by the force of repulsion. Q₁Q₂ = 4pε₀M₁M₂G but Q₂ = 12.5Q₁ = 12.5 x 4pω₀M₁M₂G ∴ Q₂ = 6.11 x 10¹⁴ Q₂ = 61.11 TC Q₁ = 4.89 TC.