Magnitude of the Charge on Each Ball

[chunkytuna21]

Two 2.5 g pith balls hang in air on cotton threads 48 cm long from a common point of support. The balls are then equally charged and they spring apart, each making an angle of 10° with the vertical. Find the magnitude of the charge on each ball.

F = (k q1 q2) / r^2

Q1 and Q2 are the same so
F = (k q^2) / r^2
q = sqrt[ (F r^2) / k ]

where r is the distance between the balls (taken as point charges)

Using cosine rule, a^2 = b^2 + c^2 - 2 b c cosA
where a = r
b and c = 0.48m
A = 10 degrees
a = sqrt( 2 * 0.48^2 - 2 * 0.48^2 * cos 10)
r = 0.0083669513m

F = force on each ball
F = mass * acceleration due to gravity * sin (5 degrees)
F = 0.0025kg * 9.81 * sin(5)
F = 2.14 * 10^-3

k = electrostatic constant = 9 * 10^9 N m^2 C^-2

so q = sqrt[ (F r^2) / k ]
q = sqrt[ (2.14 * 10^-3 x 0.0083669513^2) / 9 * 10^9]
q = sqrt( 1.664584116E-17)

q = 4.1E-9 C

I have tried almost everything, but I keep getting the wrong answer. Where am I going wrong? Am I even on the right track? Any help would be greatly appreciated.

 

[rl.bhat]

1) Each ball makes an angle 10 degrees with the vertical..
2) In equilibrium position, three forces are acting on the ball. Identify them.
3) Resolve them and equate net Fx = 0 and net Fy = 0