Exam

JEE Main

Year

2020

Date

9 January

Shift

Evening Shift

Subject

Physics

Chapter

Mechanical Properties of Fluids

JEE Main 2020 · 9 January · Evening Shift · Physics · Mechanical Properties of Fluids

A small spherical droplet of density d is floating exactly half...

A small spherical droplet of density $d$ is floating exactly half immersed in a liquid of density $ρ$ and surface tension $T .$ The radius of the droplet is (take note that the surface tension applies an upward force on the droplet):

Step-by-step solution

$dVg = p$\left(\dfrac{V}{2}\right)g + $T\left(2\pir\right)$
$⇒ d . \dfrac{4}{3}\pi{r}^{3}g = p . \dfrac{2}{3}\pi{r}^{3}g + 2\pirT$
$⇒ \dfrac{2}{3}{r}^{2}g\left(2d - p\right) = 2T$
$⇒ r = \sqrt{\dfrac{3T}{\left(2d - p\right)g}}$