Question

Drops of liquid of density p are floating in a liquid of density ${\rho }_L$. If the surface tension is T, the radius of the drop will be

• A. $\sqrt{\frac{3T}{g(3\rho -{\rho }_L)}}$
• B. $\sqrt{\frac{6T}{g(2\rho -{\rho }_L)}}$
• C. $\sqrt{\frac{3T}{g(2\rho -{\rho }_L)}}$
• D. $\sqrt{\frac{3T}{g(4\rho -3p_L)}}$

Answer 1

Answer: (C)

$\sqrt{\frac{3T}{g(2\rho -{\rho }_L)}}$

$\text{We know that}$

$f_T=T\times 2\pi r\text{.}$

So

$T\times 2\pi r+\frac{2}{3}\pi r^3{\rho }_{L}g=\frac{4}{3}\pi r^3\rho g$

$3T=(2\rho -{\rho }_L)g{r}^2$

$r=\sqrt{\frac{3T}{g(2\rho -l_L})}$

Answer:- (C)