Two uniformely charged spheres (x and y) are suspended by strings of length l from vertically adjustable supports. the spheres are in static equilibrium and at the same height, as shown below. . the angles with respect to the vertical are q=13.4°, and t=19.2°. (q is the angle between sphere x and the vertical. t is the angle between the sphere y and the vertical.) true or false:
the charge on x can be negative and that on y negative.
the charge on x can be negative and that on y positive.
the amount of charge on y can be equal to that on x.
the mass of x can be less than that of y.
the amount of charge on y can be less than that on x.

The charge on X can be negative and that on Y negative. 
TRUE if they can be repelling 

The charge on X can be negative and that on Y positive. 
TRUE if they can be attracting 

The amount of charge on Y can be equal to that on X. 
TRUE. The electrostatic forces on the spheres are going to be equal and opposite regardless of the magnitudes (Newton's Third Law). Therefore, the angle difference cannot be due to them having different charges. 

The mass of X can be less than that of Y. 
FALSE. Because Q < T, we know that the mass of X must be greater than the mass of Y. The fact that the angles are different tells us only about the masses (see the explanation immediately above). The horizontal components of the tensions in the strings must be equal. If the angles are different, it must be because the vertical components are different. To make Q smaller than T, it must have a greater vertical component for the same horizontal component. 

The amount of charge on Y can be less than that on X. 
You have a horizontal vector depending on the charge and a vertical vector depending on the weight, which we are mistakenly calling mass for this example. The horizontal force divided by the vertical force gives the tangent of the angle at which it hangs.

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