Question

Two narrow bores 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 contains 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 $7.3 \times 10^{-2} Nm ^{-1} .$ Take angle of contact $=0^{\circ}$, density of water $\left.=1.0 \times 10^{3} kgm ^{-3}, g=9.8 \,ms ^{-2}\right)$.

• A. 5 mm
• B. 6 mm
• C. 7 mm
• D. 8 mm

Answer 1

Answer: (A)

For the first bore, pressure difference between
the concave and convex sides of the meniscus $=\frac{2 S}{a_{1}}$
$=\frac{2 \times 7.3 \times 10^{-2} Nm ^{-1}}{\left(\frac{6}{2} \times 10^{-3} m \right)}=48.7 \,Pa$
Similarly, for the second bore, pressure difference
$=\frac{2 S}{a_{2}}=\frac{2 \times 7.3 \times 10^{-2} Nm ^{-1}}{\left(\frac{3}{2} \times 10^{-3}\right) m }=97.3 \,Pa$
Consequently, the level difference in the two boxes
$=\frac{\Delta P}{\rho \cdot g}=\frac{(97.3-48.7) Pa }{10^{3} kg m ^{-3} \times 9.8 ms ^{-2}}=5 \times 10^{-3}\, m =5\, mm$