Question

Two capillary tubes of diameters 3.0 mm and 6.0 mm are joined together to form a U-tube open at both ends. If the U-tube is filled with water, what is the difference in its levels in the two limbs of the tube? Surface tension of water at the temperature of the experiment is $7.3\times {10}^{-2}N/m$. Take the angle of contact to be zero and density of water to be ${10}^{3}kg/m^3(g=9.8m/s^2)$

• A. 5 mm
• B. 10 mm
• C. 15 mm
• D. 20 mm

Answer 1

The correct option is A 5 mm

$\varrho gh=\frac{2T}{R}$

$h_1=\frac{2\times 7.3\times {10}^{-2}}{{10}^3\times 9.8\times 1.5\times {10}^3}$

$h_2=\frac{2\times 7.3\times {10}^{-2}}{{10}^3\times 9.8\times 3\times {10}^{-3}}$

So $△h=h_1-h_2$

$=\frac{2\times 7.3\times {10}^{-2}}{{10}^3\times 9.8\times {10}^{-3}}(\frac{2}{3}-\frac{1}{3})$

$=\frac{2\times 7.3\times {10}^{-2}}{{10}^3\times 9.8\times 3\times {10}^{-3}}$

$△h=5mm$