Charge transfer problem

[Hexon]

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From princeton review
We have three metal sphere's in fixed positions R (+Q), S (+2Q) and T (+3Q):

+Q +2Q +3Q
*--------------**-------------------------***
R S T

The distance between R and S is d1 and distance between S and T is d2. d2 = sq. root of 3*d1.

A small metal sphere carrying a charge of -2Q is first brought into contact with the sphere at R (+Q), and then into contact with the sphere at S (+2Q) and finally into contact with sphere T (+3Q). After making contact with the three spheres, in the stated order, the charge on the sphere at T is:

A: +3Q
B: +15Q/4
C: +15Q/8
D: +4Q


Appreciate the help

 

[milski]

Every time you have two touching spheres, the charge of each of them becomes half of the combined charge.
After touching R, the charge on the small sphere is (-2Q+Q)/2=-Q/2
After touching S, the charge on the small sphere is (-Q/2+2Q)/2=3Q/4
After touching T, the charge on the small sphere is (3Q/4+3Q)/2=15Q/8

->C

 

[Hexon]

much appreciated!
thanks!