Two isolated conducting spheres $S_{1}$ and $S_{2}$ of radius $\frac{2}{3} R$ and $\frac{1}{3} R$ have $12 \mu \mathrm{C}$ and $-3 \mu \mathrm{C}$ charges, respectively, and
are at a large distance from each other. They are now connected by a conducting wire. A long time after this is done the charges on $S_{1}$ and $S_{2}$ are respectively :
Correct Option: 1
(1) Total charge $Q_{1}+Q_{2}=Q_{1}^{\prime}+Q_{2}^{\prime}$
$=12 \mu C-3 \mu C=9 \mu C$
Two isolated conducting sphres $S_{1}$ and $S_{2}$ are now connected by a conducting wire.
$\therefore V_{1}=V_{2}=\frac{K Q_{1}^{\prime}}{\frac{2}{3} R}=\frac{K Q_{2}^{\prime}}{\frac{R}{3}}=12-3=9 \mu \mathrm{C}$
$Q_{1}^{\prime}=2 Q_{2}^{\prime} \Rightarrow 2 Q_{2}^{\prime}+Q_{2}^{\prime}=9 \mu C$
$\therefore Q_{1}^{\prime}=6 \mu C$ and $Q_{2}^{\prime}=3 \mu C$