You gently place several steel needles on the free surface of the water in a large tank. The needles come in two lengths: some are 5 cm long, and some are 10 cm long. Needles of each length are available with diameters of 1 mm, 2.5 mm, and 5 mm.

Make a prediction as to which needles, if any will float.

Assume contact angle theta = 0. (For water, rho=1000kg/m3, sigma=0.0728 N/m, for steel, SG= 0.83).