Water emerges drop by drop from a dropper of orifice radius r = 5 * 10⁻⁴ m. Taking density of water rho = 10³ kg/m³, g = 10 m/s² and surface tension T = 0.11 N/m, estimate the radius of a drop at the instant it just detaches from the dropper.

1.4 * 10⁻³ m
3.3 * 10⁻³ m
2.0 * 10⁻³ m
4.1 * 10⁻³ m

Correct answer: 1.4 * 10⁻³ m

Solution

Just before detachment, the surface tension acting along the circle of contact (length 2*pi*r) supports the drop's weight. Equating the maximum upward surface-tension force to the drop's weight gives the detachment radius R.

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