JEE Main20209 Jan 2020Evening ShiftPhysicsMechanical Properties of FluidsActual
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):
Options
- Ar = 2 T 3 ( d + ρ ) g
- Br = T ( d - ρ ) g
- Cr = T ( d + ρ ) g
- Dr = 3 T ( 2 d - ρ ) g
Correct answer
D. r = 3 T ( 2 d - ρ ) g
Step-by-step solution
d V g = p V 2 g + T 2 π r ⇒ d . 4 3 π r 3 g = p . 2 3 π r 3 g + 2 π r T ⇒ 2 3 r 2 g 2 d - p = 2 T ⇒ r = 3 T 2 d - p g