Previous Year NEET Question- Electrostatics L-10

Question: Twenty seven drops of same size are charged at 220V each. They combine to form a bigger drop. Calculate the potential of the bigger drop. (NEET-2021)#

A) $1980 \mathrm{~V}$

B) $660 \mathrm{~V}$

C) $1320 \mathrm{~V}$

D) $1520 \mathrm{~V}$

Answer: $1980 \mathrm{~V}$#

Explanation#

Let charge and radius of smaller drop is $q$ and $r$ respectively

For smaller drop, $\mathrm{V}=\frac{k q}{r}=220 \mathrm{~V}$

Let $R$ be radius of bigger drop,

As volume remains the same

$\left(\frac{4}{3} \pi r^3\right) \times 27=\frac{4}{3} \pi R^3$

$\Rightarrow \mathrm{R}=3 \mathrm{r}$

Now, using charge conservation,

$\mathrm{Q}=27 \mathrm{q}$

$\mathrm{V}_{\text {big drop }}=\frac{k Q}{r}=\frac{k(27 q)}{r}=9\left(\frac{k q}{r}\right)$

$=9 \times 220=1980 \mathrm{~V}$