Question 12 of 311

Two identical conducting spheres $P$ and $S$ with charge $Q$ on each, repel each other with a force $16 \mathrm{~N}$. A third identical uncharged conducting sphere $R$ is successively brought in contact with the two spheres. The new force of repulsion between $\mathrm{P}$ and $\mathrm{S}$ is :

A$1 \mathrm{~N}$B$6 \mathrm{~N}$C$12 \mathrm{~N}$D$4 \mathrm{~N}$

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Answer: (B) $6 \mathrm{~N}$

$\begin{aligned}
& F_{P S} \propto Q^2 \\
& F_{P S}=16 \mathrm{~N}
\end{aligned}$
Now If $\mathrm{P} ~\&~ \mathrm{R}$ are brought in contact then

Now If $S \& R$ are brought in contact then

New force between $P ~\&~ S$ is :
$\begin{aligned}
& \mathrm{F}_{\mathrm{PS}} \propto \frac{\mathrm{Q}}{2} \times \frac{3 \mathrm{Q}}{4} \\
& \mathrm{~F}_{\mathrm{PS}} \propto \frac{3 \mathrm{Q}^2}{8}=\frac{3}{8} \times 16=6 \mathrm{~N}
\end{aligned}$