Question 98: Properties of Matter

Question

A drop of liquid of density $$ho$$ is floating half immersed in a liquid of density $${\sigma}$$ and surface tension $$7.5 	imes 10^{-4}$$ Ncm$$-$$1. The radius of drop in $$\mathrm{cm}$$ will be :
(g = 10 ms$$-$$2)

Accepted Answer

At equilibrium, forces balance each other
$$
\mathrm{S}(2 \pi \mathrm{r})+\mathrm{F}_{\mathrm{b}}=m g
$$
Where $S=$ surface tension
$$
\begin{aligned}
& \mathrm{F}_{\mathrm{b}}=	ext { buoyant force }=\frac{2}{3} \pi r^3 \sigma g \\
& S(2 \pi r)=m g-\mathrm{F}_b=\frac{4}{3} \pi r^3\left(p-\frac{\sigma}{2}ight) g \\
& \Rightarrow r^2=\frac{3 S}{(2 p-\sigma) g} \\
& \Rightarrow r^2 =\frac{3 	imes 7.5 	imes 10^{-2}}{(2 p-\sigma) 10} \\
& \Rightarrow r^2 =\frac{22.5 	imes 10^{-2}}{(2 p-\sigma) 10}
\end{aligned}
$$
$$ \Rightarrow $$ $$
r=\frac{1.5 	imes 10^{-1}}{\sqrt{2 p-\sigma}} \mathrm{m}$$
$$=\frac{15}{\sqrt{2 p-\sigma}} \mathrm{cm}
$$

Answer

$$
\frac{15}{\sqrt{(2 \rho-\sigma)}}
$$

Answer

$$\frac{15}{\sqrt{(\rho-\sigma)}}$$

Answer

$$\frac{3}{2 \sqrt{(\rho-\sigma)}}$$

Answer

$$\frac{3}{20 \sqrt{(2 \rho-\sigma)}}$$

Properties of Matter

A drop of liquid of density $\rho is floating half immersed in a liquid of density {\sigma} and surface tension 7.5 \times 10^{-4} Ncm-1. The radius of drop in \mathrm{cm} will be : (g = 10 ms-$2)

Choose the correct answer: