Question

The potential of a large liquid drop when eight liquid drops are combined is $20V$. 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
$\left(\frac{4}{3}\pi r^3\right)\times 8=\frac{4}{3}\pi R^3$
$\Rightarrow 2r=R\dots (i)$
According to charge conservation
$8q=Q\dots (ii)$
Potential of one small drop $\left(V^{\prime }\right)=\frac{q}{4\pi {\epsilon }_{0}r}$
Similarly, potential of big drop (V) $=\frac{Q}{4\pi {\epsilon }_{0}R}$
Now, $\frac{V^{\prime }}{V}=\frac{q}{Q}+\frac{R}{r}$
$\Rightarrow \frac{V^{\prime }}{20}=\frac{q}{8q}\times \frac{2r}{r}$ [from Eqs. (i) and (ii)]
$\therefore V^{\prime }=5$ volt