Question

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

• A. 10V
• B. 7.5V
• C. 5V
• D. 2.5V

Answer 1

Answer: (C)

Volume of 8 small drops = Volume of big drop
$\therefore \left(\frac{4}{3}\pi r^3\right)\times 8=\frac{4}{3}\pi R^3$
$\Rightarrow 2r=R$ ....(i)
According to charge conservation
$8q=Q$ ....(ii)
Potential of one small drop $\left(V^{\prime }\right)=\frac{q}{4\pi {\epsilon }_{0}r}$
Similarly, potential of big drop $\left(V\right)=\frac{Q}{4\pi {\epsilon }_{0}R}$
Now, $\frac{V^{\prime }}{V}=\frac{q}{Q}\times \frac{R}{r}$
$\Rightarrow \frac{V^{\prime }}{20}=\frac{9}{8q}\times \frac{2r}{r}$
[from Eqs. (i) and (ii)]
$\therefore V^{\prime }=5V$