Question

Each of 27 identical spherical drops of a conducting liquid is charged upto a potential of Vo. They coal ease to form a bigger drop. What is the potential on the surface of this bigger drop.

• A. $9V^{\circ }$
• B. $3V^{\circ }$
• C. $27V^{\circ }$
• D. $V^{\circ }$

Answer 1

The correct option is A $9V^{\circ }$

If $q$ be the charge on each drop, charge on big drop is $Q=27q$

If $R$ be the radius of bigger drop.

$\begin{array}{c}\frac{4}{3}\pi R^3=27\left(\frac{4}{3}\pi R^3\right)\\ \Rightarrow R=3r\\ \therefore V_1=k\frac{q}{r}\\ and{V}_2=k\frac{Q}{R}=R\frac{27q}{3r}=9V_1\\ \therefore \frac{V_2}{V_1}=9\end{array}$

Hence, Option $A$ is correct.