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Two identical conducting spheres $\mathrm{P}$ and $\mathrm{S}$ with charge $Q$ on each, repel each other with a force $16 \mathrm{~N}$. A third identical uncharged conducting sphere $\mathrm{R}$ is successively brought in contact with the two spheres. The new force of repulsion between $\mathrm{P}$ and $\mathrm{S}$ is :
$4 \mathrm{~N}$
$6 \mathrm{~N}$
$1 \mathrm{~N}$
$12 \mathrm{~N}$
Solution
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$F_{P S} \propto Q^2$
$F_{P S}=16 N$
Now If $\mathrm{P} \& \mathrm{R}$ are brought in contact then
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Now If $\mathrm{S} \& \mathrm{R}$ are brought in contact then
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New force between $P \& S$ is :
$\mathrm{F}_{\mathrm{PS}} \propto \frac{\mathrm{Q}}{2} \times \frac{3 \mathrm{Q}}{4}$
$\mathrm{~F}_{\mathrm{PS}} \propto \frac{3 \mathrm{Q}^2}{8}=\frac{3}{8} \times 16=6$
