Finding the Angle Between Two Charged Spheres Using Coulomb's Law

[seto6]

Homework Statement

The figure shows two 5.0 g spheres suspended from 1.0-m-long threads. The spheres repel each other after being charged to +31 nC. What is the angle θ ?

Homework Equations

The Attempt at a Solution

i tried it by writing equation in the x and y component for one of the ball and then i would have two unknowns tension and the radius.

now for sin (theta) = r/1
cos (theta) = sqrt(1-r^2)

so for the columbs force the radius would be 2r.

now i solved for r = 4.4108*10^(-5)

this doesn't make sense, i would get the angle to be 2.53*10^(-3)

but the choice for the angles are :

Thanks for helping

 

[rl.bhat]

It T is the tension in the string, then
Tsinθ = F

Tcosθ = mg

tanθ = 9*10^9*(31*10^-9)^2/r^2*5*10^-3*9.8

Since θ is very small, tanθ is nearly equal to θ = r

So r^3 = (θ)^3 = 9*10^9*(31*10^-9)^2/5*10^-3*9.8

Now solve to find θ.