Two small metallic spheres, each of mass 0.20 g, are suspended as pendulums by l

Question

Two small metallic spheres, each of mass 0.20 g, are suspended as pendulums by light strings from a common point as shown in the figure below. The spheres are given the same electric charge, and it is found that they come to equilibrium when each string is at an angle of 7.0

Two small metallic spheres, each of mass 0.20 g, are suspended as pendulums by light strings from a common point as shown in the figure below. The spheres are given the same electric charge, and it is found that they come to equilibrium when each string is at an angle of 7.0 degree with the vertical. If each string is 30.0 cm long, what is the magnitude of the charge on each sphere? Your response differs from the correct answer by more than 10%. Double check your calculations. C

Explanation / Answer

mass of two spheres is m = 0.20 g = 0.20 x 10^-3 kg

angle made by each string is theta = 7.0o = 7.0 x (pi/180) radians

length of each string is L = 30.0 cm = 30.0 x 10^-2 m

let q be the charge on each sphere

the distance between the spheres is

S = L x theta

the gravitational force between the spheres is

F = (Gm^2/S^2)

where G = 6.67 x 10^-11 Nm^2/kg^2

the electric force between the spheres is

Fe = (kq^2/S^2)

where k = (1/4pi x e_o) = 9 x 10^9 Nm^2/C^2

here,Fe = F

or (kq^2/S^2) = (Gm^2/S^2)

or kq^2 = Gm^2

or q^2 = (Gm^2/k)

or q = (G/k)^1/2 x m

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