The potential of a large liquid drop when eight liquid drops are...

Volume of eight drops = Volume of a big drop $\therefore \quad\left(\frac{4}{3} \pi r^3\right) \times 8=\frac{4}{3} \pi R^3\Rightarrow \quad 2 r=R$...(i) According to charge conservation, $8 q=Q$...(ii) Potential of one small drop, $V^{\prime}=\frac{q}{4 \pi \varepsilon_0 r}$ Similarly, potential of big drop, $V=\frac{Q}{4 \pi \varepsilon_0 R}$ Now, $\quad \frac{V^{\prime}}{V}=\frac{q}{Q} \times \frac{R}{r}\Rightarrow \quad \frac{V^{\prime}}{20}=\frac{q}{8 q} \times \frac{2 r}{r} \quad$ [from Eqs. (i) and (ii)] $\therefore \quad V^{\prime}=5 \mathrm{ V}$