Question

Eight identical spherical mercury drops charged to a potential of $20V$ each are coalesced into a single spherical drop.

• A. The internal Energy of the system remains the same.
• B. The new potential of the drop is $80V$
• C. Internal energy of the system decreases
• D. The potential remains the same i.e., $20V$

Answer 1

The correct option is B The new potential of the drop is $80V$

Potential of one small drop of mercury,
$V=\frac{kq}{r}=20V$
Volume of big drop=volume of $8$ small drops
$\frac{4}{3}\pi R^3=8\times \frac{4}{3}\pi r^3\Rightarrow =2r$
$Q^{\prime }=8q$
Potential of big drop,
$V^{\prime }=\frac{k{Q}^{\prime }}{R}=\frac{K\times 8q}{2r}=\frac{4kq}{r}=4\times 20=80V$
Hence, option $B$ is the correct answer.