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Liquid medicine of density rho is dispensed into the eye using a dropper. Pressing the bulb forms a drop at the opening. Assume the drop is spherical (minimum surface energy) and detaches when the upward vertical force from surface tension T becomes less than its weight. If the radius of the dropper opening is r and the drop radius is R (with r << R), find the vertical force due to surface tension acting on the drop.
- 2*pi*r*T
- 2*pi*R*T
- 2*pi*r²*T/R
- 2*pi*R²*T/r
Correct answer: 2*pi*r²*T/R
Solution
Surface tension force acts along the rim of radius r: F = T * (2*pi*r), directed tangent to the drop surface. The vertical component is F*sin(theta) where sin(theta) ~ r/R for a sphere of radius R meeting the small opening of radius r. Thus the vertical force = 2*pi*r*T*(r/R) = 2*pi*r²*T/R.
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