A cylindrical capillary tube of radius 0.2 mm is made by joining two capillaries and of different materials having water contact angles of and , respectively. The capillary tube is dipped vertically in water in two different configurations, case I and

Question

A cylindrical capillary tube of radius 0.2 mm is made by joining two capillaries $T_{1}$ and $T_{2}$ of different materials having water contact angles of $0 °$ and $60 °$ , respectively. The capillary tube is dipped vertically in water in two different configurations, case I and II as shown in figure. Which of the following option(s) is (are) correct

[Surface tension of water $= 0.075 N/m$ , density of water $= 1000 {kg/m}^{3}, g = 10 {m/s}^{2}$ ] [2019]

Smart Achievers · Accepted Answer

(1, 2, 3)

$For case I$

$h_{1} = \frac{2 T \cos θ_{1}}{r ρ g} = \frac{2 \times 0.75 \times \cos 0 °}{2 \times 10^{- 4} \times 1000 \times 10} = 7.5 cm$

$For case II$

$h_{2} = \frac{2 T \cos θ_{2}}{r ρ g} = \frac{2 \times 0.75 \times \cos 60 °}{2 \times 10^{- 4} \times 1000 \times 10} = 3.75 cm$

The correction in the height of water column raised in the tube, due to weight of water contained in the meniscus will be different for both cases.

In case II, if the capillary joint is 5 cm above the water surface then water in capillary will not reach the interface.

Water will reach only till 3.75 cm.

Solution

1 The correction in the height of water column raised in the tube, due to weight of water contained in the meniscus, will be different for both cases.

2 For case II, if the capillary joint is 5 cm above the water surface, the height of water column raised in the tube will be 3.75 cm. (Neglect the weight of water in the meniscus).

3 For case I, if the joint is kept at 8 cm above the water surface, the height of water column in the tube will be 7.5 cm. (Neglect the weight of the water in the meniscus.)

4 For case I, if the capillary joint is 5 cm above the water surface, the height of water column raised in the tube will be more than 8.75 cm. (Neglect the weight of water in the meniscus.)

Want Us to Email you About Special Offers & Updates?