Question: Q. 18. Eight identical spherical drops, each carrying a charge $1 n \mathrm{C}$ are at a potential of $900 \mathrm{~V}$ each. All these drops combine together to form a single large drop. Calculate the potential of this large drop.
(Assume no wastage of any kind and take the capacitance of a sphere of radius $r$ as proportional to $r$ ).
U] [CBSE SQP 2014]
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Solution:
Ans. Let the radius of each drop be $r$. The capacitance $C$ of each drop is $k r$, where $k$ is a constant.
Also $q=C V, V=900$ volt
$\therefore$ Charge on each drop $=q=(k r \times 900) C \quad 1 / 2$ $\therefore$ Total charge on all the eight drops $=Q=8 q$
$$ =7200 \mathrm{kr} \mathrm{1/2} $$
Let $R$ be the radius of the large drop. Then
$$ \begin{array}{rlrl} \frac{4 \pi}{3} R^{3} & =8 \times \frac{4 \pi}{3} r^{3} \ \therefore \quad & R & =(8)^{1 / 3} r=2 r \end{array} $$
$\therefore$ Capacitance $C^{\prime}$ of the large drop $=k \mathrm{R}=2 k r \quad 1 / 2$
$\therefore$ Potential of the large drop $=\frac{Q}{C^{\prime}}=\frac{7200 k r}{2 k r}$ volt
$$ =3600 \mathrm{~V} $$
[CBSE Marking Scheme 2014]
