Question

The potential of a large liquid drop when eight liquid drops are combined is $20\,V$. Then the pontential of each single drop was

• A. 2.5 V
• B. 5 V
• C. 7.5 V
• D. 10 V

Answer 1

Answer: (B)

Volume of 8 drops = volume of big drop
$\left(\frac{4}{3} \pi r^{3}\right) \times 8=\frac{4}{3} \pi R^{3}$
$\Rightarrow 2 r=R\,\,\,\,\,\dots(i)$
According to charge conservation
$8 q=Q\,\,\,\,\,\dots(ii)$
Potential of one small drop $\left(V'\right)=\frac{q}{4 \pi \varepsilon_{0} r}$
Similarly, potential of big drop (V) $=\frac{Q}{4 \pi \varepsilon_{0} R}$
Now, $ \frac{V'}{V}=\frac{q}{Q}+\frac{R}{r}$
$\Rightarrow \frac{V'}{20}=\frac{q}{8 q} \times \frac{2 r}{r}$ [from Eqs. (i) and (ii)]
$\therefore V'=5 $ volt