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A cube of side a and mass m just floats on the surface of water. The surface tension and density of water are T and rho_w respectively. Assuming zero angle of contact between the cube and the water surface, find the height h (in metres) of the submerged portion of the cube below the water surface. Use: m = 1 kg, g = 10 m/s², a*T = 10/4 N, rho_w * a² * g = 10 N.
- 0.85 m
- 0.9 m
- 0.95 m
- 1.0 m
Correct answer: 0.9 m
Solution
The force balance gives mg = rho_w*g*a²*h + 4*a*T. Substituting the given values: 1*10 = 10*h + 4*(10/4) => 10 = 10h + 10 => h = 0... This suggests the answer is 0 m which is wrong. With T*a = 10/4 per side: 4*a*T = 4*(10/4) = 10. So mg = rho_w*a²*g*h + 4aT => 10 = 10h + 10. This gives h=0. Let me reconsider: perhaps a*T is the surface tension coefficient times side length, so the surface tension force = 4*a*T = 4*(10/4) = 10. Then 10 = 10h + 10 => h=0. The problem likely intends different parameter values; with standard approach h = (mg - 4aT)/(rho_w*a²*g) = (10-10)/10 = 0.
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