125 identical charged small spheres coalesce to form a big charged sphere, If the electric potential on each…

125 identical charged small spheres coalesce to form a big charged sphere, If the electric potential on each small sphere is 60 mV then the electric potential on the bigger sphere formed is
  1. 30 V
  2. 15 V
  3. 1.5 V
  4. 3 V

Solution

$\frac{\mathrm{kq}}{\mathrm{r}}=60 \mathrm{mV}$ $\mathrm{V}_{\mathrm{i}}=\mathrm{V}_{\mathrm{f}} \Rightarrow\left(\frac{4}{3} \pi \mathrm{r}^3\right) \times 125=\frac{4}{3} \pi \mathrm{R}^3 \Rightarrow \mathrm{R}=5 \mathrm{r}$
Also, $Q=125 \mathrm{q}$ $\begin{aligned} & \therefore \text { Potential on big drop, } \mathrm{V}=\frac{\mathrm{KQ}}{\mathrm{R}}=\frac{\mathrm{k}(125 \mathrm{q})}{5 \mathrm{r}} \\ & =25\left(\frac{\mathrm{~kg}}{\mathrm{r}}\right)=25 \times 60 \times 10^{-3} \\ & =1.5 \mathrm{~V} \end{aligned}$

Asked in: AP EAMCET 2024 (23 May Shift 1)

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