A liquid drop of density ' $Q$ ' is floating half immersed in a liquid of density ' $d$ '. Diameter of the…

A liquid drop of density ' $Q$ ' is floating half immersed in a liquid of density ' $d$ '. Diameter of the liquid drop is ( $\mathrm{Q}>\mathrm{d}, \mathrm{g}=$ acceleration due to gravity, $\mathrm{T}=$ surface tension)
  1. $\left[\frac{3 T}{g(2 Q-d)}\right]^{\frac{1}{2}}$
  2. $\left[\frac{6 T}{g(Q-d)}\right]^{\frac{1}{2}}$
  3. $\left[\frac{12 \mathrm{~T}}{\mathrm{~g}(2 \mathrm{Q}-\mathrm{d})}\right]^{\frac{1}{2}}$
  4. $\left[\frac{9 T}{g(Q-d)}\right]^{\frac{1}{2}}$

Solution

The force balance invovles, surface-tension force and boyancy force balance the weight of the droplet, so the equation is: $(2 \pi r) T+\left(\frac{4}{3} \pi r^3\right) \mathrm{dg}=\left(\frac{4}{3} \pi r^3\right) \mathrm{Qg}$ Where, $\mathrm{r}$ is the radius of the drop, $\mathrm{T}$ the interfacial tension between the liquids, $g$ is acceleration due to gravity. Therefore, $\mathrm{T}=\left(\frac{2}{3} \mathrm{r}^2\right)(\mathrm{Q}-\mathrm{d}) \mathrm{g}$ Diameter $=2 r=\left[\frac{6 T}{g(Q-d)}\right]^{\frac{1}{2}}$. .

Asked in: MHT CET 2022 (05 Aug Shift 2)

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