Question

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

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

Answer 1

Answer: (C)

$5V$

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, $\frac{V^{\prime }}{V}=\frac{q}{Q}\times \frac{R}{r}\Rightarrow \frac{V^{\prime }}{20}=\frac{q}{8q}\times \frac{2r}{r}$
$\therefore V^{\prime }=5V$