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An open capillary tube is dipped into a vessel of mercury. The mercury level inside the capillary sits below the level in the vessel by Dh = 4.6 mm. Given the surface tension of mercury is 0.46 N/m and its density is 13.6 g/cc, find the radius of curvature of the mercury meniscus in the tube.

1. 1/340 m
2. 1/680 m
3. 1/1020 m
4. Information insufficient

Correct answer: 1/680 m

Solution

For mercury (non-wetting) the meniscus is convex and depressed. Pressure balance gives 2*S/r = rho*g*Dh, so r = 2*S/(rho*g*Dh) = 2*0.46/(13600*9.8*0.0046) = 0.92/613.1 ~ 1.5e-3 m = 1/680 m approximately.

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