Please help me solve this problem Imagine a small metal sphere floating on water

Question

Please help me solve this problem

Imagine a small metal sphere floating on water. Assume this is purely due to surface tension effects (ignore buoyancy). What is the maximum diameter of this sphere such that it, in fact, floats? What keyword in the first sentence of this problem suggests that the buoyancy force acting on this sphere might be negligible, arid why? According to your analysis, are smaller or larger spheres more likely to float? Let us take P sphere = 7800 kg/m^3, sigma w = 0.073 N/m.

Explanation / Answer

apply Weight W   = Force = mg = surface tension * Circurference

also density D = MASS/Voulme

mass = dV

denisty *V * g = sigma w * 2pi r

V/r    = 2*3.14* 0.073 / (7800*9.8)

4* pi r^3/3r   =   6 e -6

r^2 = 3 * 6e-6 */(4*3.14)

r^2 = 1.43 e -6

r = 1.19mm

do diameter = d = 2 r = 1.19 mm*2

D = 2.4 mm is the diamter of the sphere

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