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A metal wire of diameter d lies horizontally on a water surface. Taking T as the surface tension and rho as the wire's density, the greatest length L of the wire for which it will still not sink is:
- sqrt(2T/(pi*d*rho*g))
- sqrt(2T*g/(pi*d))
- sqrt(2*pi*d/(T*g))
- any length
Correct answer: any length
Solution
Surface tension supports the wire along both contact lines: F = T*(2L) = 2*T*L. Weight W = (mass)*g = rho*(pi*(d/2)²*L)*g = rho*pi*d²*L*g/4. Both F and W are proportional to L, so L cancels in the balance condition (2T = rho*pi*d²*g/4). Whether the wire floats depends only on d (and T, rho), not on L. Hence if the diameter satisfies the condition, any length floats.
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