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 × 10-2 Nm -1 . Take angle of contact =0°, density of water .=1.0 × 103 kgm -3, g=9.8 ms -2).

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 × 10-2 Nm -1 . Take angle of contact =0°, density of water .=1.0 × 103 kgm -3, g=9.8 ms -2). (A) 5 mm (B) 6 mm (C) 7 mm (D) 8 mm

Tardigrade Admin · Accepted Answer

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 1 0 ^{- 2} N m ^{- 1}}{( \frac{6}{2} \times 1 0 ^{- 3} m )} = 48.7 P a

Similarly, for the second bore, pressure difference

= \frac{2 S}{a _{2}} = \frac{2 \times 7.3 \times 1 0 ^{- 2} N m ^{- 1}}{( \frac{3}{2} \times 1 0 ^{- 3} ) m} = 97.3 P a

Consequently, the level difference in the two boxes

= \frac{Δ P}{ρ \cdot g} = \frac{( 97.3 - 48.7 ) P a}{1 0 ^{3} k g m ^{- 3} \times 9.8 m s ^{- 2}} = 5 \times 1 0^{- 3} m = 5 mm