q1=q2 & L1=L2 for Equal Level Charged Pendulum

[THE BEAST]

1. Two small spheres with masses m1 and m2 hang on weightless, insulating threads of length L1 and L2. The two spheres carry charges of q1 and q2 (like charges) respectively. The spheres hang such that they are at the same level with one another. The threads are inclined at angle theta 1 and theta 2 with the vertical. The angle theta 1 will be equal to theta 2 when which of the following must be equal, m1=m2 or q1=q2 or L1=L2?

Homework Equations

= i tried to use the tension force, so t cos(theta)= mg - (1)
t sin(theta)= F - (2)[/B]

The Attempt at a Solution

= [/B]
okay. let's see. I think the most important sentence here is that the spheres hang such that they are the same level with one another. Now i tried to think in terms of tension. So, the Force applied due to repulsion is equal to the horizontal component of the tension. Now, since the electrical force applied on both the spheres is same, so for the spheres to be at same level, L1 needs to be equal to L2.
But i can't figure out what to do with the mass. I mean the weight of the bob doesn't really affect the swing right? i haven't revised mechanics for a long time, so i might have forgotten everything about pendulum.
Now, about the q1= q2, i don't think the magnitude of charges really matter. I mean the electrical force applied on both the spheres will be same, so we don't need it to be of same magnitude. Can this point be proven mathematically?

 

[Dr. Courtney]

You need a good picture for this one.

 

[THE BEAST]

by picture, you mean a diagram?

 

[THE BEAST]

here's the diagram.

 

[haruspex]

The question as stated doesn't specify that the suspension points are at the same level. Your diagram assumes they're suspended from the same point. I'll assume that's right.
If they are suspended from the same level, and the angles are the same, and the masses are on the same level, doesn't L1=L2 follow from simple geometry?
It's not clear from the question whether you are supposed to pick one of the three options or list all that necessarily hold. If the latter, the question now becomes whether you can deduce the masses to be equal, or the charges to be equal, or both.
Draw a FBD for one mass. As you say, the electrical repulsion must be the same for both. Consider the horizontal and vertical balances of forces. What is the relationship between the repulsion, the gravitational force, and the angle?

 

[rude man]

I would assume that L1 can be ≠ L2 (different-height ceilings).
Hint 1: does it matter if L1 = L2 or not?
Hint 2: pick only one among L1 = L2, m1 = m2 or q1 = q2.