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Q.

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)

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a

r=2T3d+ρg

b

r=Td+ρg

c

r=Td−ρg

d

r=3T2d−ρg

answer is D.

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Detailed Solution

Weight is balanced by Buoyancy force &surface tension forces ⇒mg=FB+FST⇒mg=Vimρg+T×2πR ⇒Vdg=V2ρg+T×2πR⇒Vd−ρ2g=T×2πR ⇒43πR32d−ρ2g=T×2πR ⇒R=3T2d−ρg

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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)