Question

Eight identical spherical mercury drops charged to a potential of 20 v 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 80 V
• C. Internal Energy of he system decreases
• D. The potential remains the same i.e. 20 v

Answer 1

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

$V=\frac{kq}{r}=20V$
$\frac{4}{3}\pi R^3=8\times \frac{4}{3}\pi r^3\Rightarrow R=2r$
$Q^{\prime }=8q$
$V^{\prime }=\frac{k{Q}^{\prime }}{R}=\frac{k\times 8q}{2r}=\frac{4kq}{r}=4\times 20$

$V^{\prime }=80V$