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)

5V

Answer 2

Volume of 8 small drops = Volume of big drop
$\therefore\left(\frac{4}{3}\pi r^{3}\right) \times8 = \frac{4}{3}\pi R^{3}$
$\Rightarrow 2r =R$ ....(i)
According to charge conservation
$8q = Q$ ....(ii)
Potential of one small drop $\left(V'\right) = \frac{q}{4\pi\varepsilon_{0}r}$
Similarly, potential of big drop $\left(V\right)= \frac{Q}{4\pi\varepsilon_{0}R}$
Now, $\frac{V'}{V} = \frac{q}{Q}\times\frac{R}{r}$
$\Rightarrow \frac{V'}{20} = \frac{9}{8q}\times\frac{2r}{r}$
[from Eqs. (i) and (ii)]
$\therefore V' = 5\,V$