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A spherical drop of liquid splits into 1000 identical spherical drops. If u_{\mathrm{i}} is the surface energy of the original drop and u_{\mathrm{f}} is the total surface energy of the resulting drops, the (ignoring evaporation), \frac{u_f}{u_i}=$ $\left(\frac{10}{x}\right). Then value of x is _________.

Option: 1

1


Option: 2

-


Option: 3

-


Option: 4

-


Answers (1)

best_answer

 Surface Tension =T
R: Radius of a bigger drop
r: Radius of smaller drop
The volume will remain the same

\begin{aligned} & \frac{4}{3} \pi \mathrm{R}^3=1000 \times \frac{4}{3} \pi \mathrm{r}^3 \\ & \mathrm{R}=10 \mathrm{r} \\ & \mathrm{u}_{\mathrm{i}}=\mathrm{T} \cdot 4 \pi \mathrm{R}^2 \\ & \mathrm{u}_{\mathrm{f}}=\mathrm{T} \cdot 4 \pi \mathrm{r}^2 \times 1000 \\ & \frac{\mathrm{u}_{\mathrm{f}}}{\mathrm{u}_{\mathrm{i}}}=\frac{1000 \mathrm{r}^2}{\mathrm{R}^2} \\ & \frac{\mathrm{u}_{\mathrm{f}}}{\mathrm{u}_{\mathrm{i}}}=\frac{10}{1} \\ & \text { So, } x=1 \end{aligned}

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vishal kumar

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