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

The correct option is (A) $10V$
According to the question 8 drops are joined to form a big drop

So,

Volume of $8$ drops $=$ Volume of big drop
$\therefore \left(\frac{4}{3}\pi r^3\right)\times 8=\frac{4}{3}\pi R^3$

After solving
$\Rightarrow 2r=R....\left(i\right)$

If each small drop has charge q then according to charge conservation
$8q=Q....\left(ii\right)$
We know,
$V\propto \frac{1}{r}$

So we can write
or $\frac{V_1}{V_2}=\frac{r_2}{n}$

Or,
$\Rightarrow \frac{20}{V_2}=\frac{2r}{r}$

Therefore
$\Rightarrow V_2=10V$

Potential of the small drop is 10 V