Two small metallic spheres with equal mass are suspended as pendulums by strings of length l. the spheres have the same electric charge and come to equilibrium with each string at an angle of θ = 10.00° with the vertical. what happens if the electric charges are increased? a) θ decrease b) θ increase eliminate c) θ remains the same d) distant between spheres decreases

You have to understand the conditions of the problem. Theta is measured with the vertical, not the horizontal. The givens are

Theta is measured with the vertical

The charges are equal (an assumption)

The masses are equal (Given)

Discussion A and D

The problem with A is that it is closely connected to D. When you increase the charge, the force will go up. To compensate for the increase in force, the distance will have to increase between the 2 charged bodies. Either A is true and D is true or they both are false. In this case, both are false. You yourself eliminated D. So A goes with it.

Discussion on C  

Nothing remains the same once you increase the Charge. C cannot be the answer. When the charge is increased, the Force is unbalanced and to balance it, the distance will increase. So C will be wrong because everything changes.

B is the answer. If the only way to balance the force is to increase the distance, it will mean that theta increases as well.

c.the charges if the proton and electron and gravity