Question

We have three identical metallic spheres $A, B$, and $C$. $A$ is given a charge $Q$, and $B$ and $C$ are uncharged. The following processes of touching of two spheres are carried out in succession. Each process is carried out with sufficient time.
i. $A$ and $B$
ii. $B$ and $C$
iii. $C$ and $A$
iv. $A$ and $B$
v. $B$ and $C$
The final charges on the spheres are

• A. $\frac{11 Q}{32}, \frac{5 Q}{16}, \frac{11 Q}{32}$
• B. $\frac{11 Q}{32}, \frac{11 Q}{32}, \frac{5 Q}{16}$
• C. $\frac{8 Q}{8}, \frac{5 Q}{16}, \frac{5 Q}{16}$
• D. $\frac{5 Q}{16}, \frac{11 Q}{32}, \frac{11 Q}{32}$

Answer 1

Answer: (D)

Let us proceed process-wise. After each process the charge of spheres $A, B$ and $C$ is given below.
(i) $Q / 2, Q / 2,0$
(ii) $Q / 2, Q / 4, Q / 4$
(iii) $3 Q / 8, Q / 4,3 Q / 8$
(iv) $5 Q / 16,5 Q / 16,3 Q / 8$
(v) $5 Q / 16,11 Q / 32,11 Q / 32$