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

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) $3Q/8,Q/4,3Q/8$
(iv) $5Q/16,5Q/16,3Q/8$
(v) $5Q/16,11Q/32,11Q/32$