Only one of three balls A, B, and C carriers a net charge q . The balls are made

Question

Only one of three balls A, B, and C carriers a net charge q. The balls are made from conducting material and are identical. One of the uncharged balls can become charged by touching one ball to another then separating the two. This process of touching one ball to another and then separating the two balls can be repeated over and over again, with the result that the three balls can take on a variety of charges. Which one of the following distributions of charges could NOT possibly be achieved in this fashion, even if the process were repeated a large number of times?

A) qA = 1/3q, qB = 1/3q, qC= 1/3q

B) qA = 1/2q, qB = 1/4q, qC = 1/4q

C) qA = 1/2q, qB = 3/8q, qC = 1/4 q

D) qA = 3/8q, qB= 3/8q, qC = 1/4q

I'm pretty sure that I know the correct answer, but I'm not sure how to explain the answer, help?

Explanation / Answer

1. this can be easily achieve by make all the ball contact with each other. 2. assume A is the ball which initially has the charge of q. A+B (A touches B) 1/2 1/2 then B+C 1/4 1/4 3. this cant be achieve be cause qA+qB+qC always equal to q but in this possibility qA + qB + qC = 9q/8 4. A+B 1/2 1/2 B+C 1/4 1/4 B+A 3/8 3/8. so only 3 is unachievable.

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