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Two thin capillary tubes of diameters 5.0 mm and 8.0 mm are joined to form a U-tube that is open at both ends and contains water. Taking surface tension T = 7.3*10⁻² N/m, contact angle = 0, g = 10 m/s² and water density = 1.0*10³ kg/m³, find the difference between the water levels in the two limbs.
- 3.62 mm
- 2.19 mm
- 5.34 mm
- 4.97 mm
Correct answer: 2.19 mm
Solution
Capillary rise h = 2*T*cos(0)/(rho*g*r) = 2*T/(rho*g*r). For r1 = 2.5 mm = 2.5*10⁻³ m: h1 = 2*7.3*10⁻²/(1000*10*2.5*10⁻³) = 5.84*10⁻³ m. For r2 = 4.0*10⁻³ m: h2 = 2*7.3*10⁻²/(1000*10*4.0*10⁻³) = 3.65*10⁻³ m. Difference = h1 - h2 = 2.19*10⁻³ m = 2.19 mm.
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