Estimating the Ratio of theta1 & theta2: Two Spheres with Unequal Charges

[iknownth]

Two spheres S1 and S2 hang from light insulating strings of the same length from points P1 and P2 which are on the same level. S1 is of mass M and has charge Q. S2 is of mass M and has charge 2Q. Repulsion between S1 and S2 causes their strings to be inclined at angles of theta1 and theta2 to the vertical respectively. What is the estimated ratio of theta1/theta2?
The ans is 1.
Is it because P1 and P2 are on the same level and the two strings are of the same length?
But the charges of the two spheres are different. Shouldn't one of them be repelled further?

 

[Jasso]

What is the magnitude of the force from S1 to S2, and what is the magnitude of the force from S2 to S1?

 

[iknownth]

The force from S2 to S1 should be double that of the force from S1 to S2 because S2 has charge 2Q??

 

[ap123]

Have another look at Coulomb's law and compare the 2 electric forces.
Also think about Newton's 3rd law.

 

[Nickie]

The estimated ratio of theta1/theta2 is 1 because the two spheres have the same mass and are hanging from strings of the same length. This means that the tension in the strings will be equal, regardless of the difference in charge between the two spheres. Therefore, the repulsion between the two spheres will cause the strings to be inclined at equal angles to the vertical. The difference in charge between the two spheres will not affect the ratio of the angles.