A straight metal wire of length 10 cm rests horizontally on the surface of water. If the surface tension of water is 0.07 N m ⁻¹ and the acceleration due to gravity is 10 m s ⁻² , what is the maximum mass of the wire that can be supported by surface tension alone without sinking?

Step-by-step solution

For a straight wire resting on a liquid surface, the liquid is in contact with both sides of the wire's length. Effective length of contact, L_ eff = 2L Upward force due to surface tension, F = T L_ eff = T 2L For the wire to be supported without sinking, this upward force must balance the downward weight of the wire ( W = mg ). mg = 2TL m = 2TL g Given: T = 0.07 N m ⁻¹ L = 10 cm = 0.1 m g = 10 m s ⁻² m = 2 0.07 0.1 10 = 0.014 10 = 0.0014 kg Converting to grams: m = 0.0014 1000 g = 1.4 g Answer: 1.4 g