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A small spherical droplet of density d is floating with exactly half its volume submerged in a liquid of density rho and surface tension T. Given that surface tension exerts an upward force on the droplet at the contact line, find the radius r of the droplet.

1. r = sqrt(2T / (3*(d + rho)*g))
2. r = sqrt(3T / ((2d - rho)*g))
3. r = sqrt(T / ((d - rho)*g))
4. r = sqrt(T / ((d + rho)*g))

Correct answer: r = sqrt(3T / ((2d - rho)*g))

Solution

Balancing forces gives (4/3)*pi*r³*d*g = (2/3)*pi*r³*rho*g + 2*pi*r*T, which simplifies to r² = 3T / ((2d - rho)*g).

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