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Q.

A cylindrical capillary tube of 0.2mm radius is made by joining two capillaries $T_{1}$ and $T_{2}$ of different materials having water contact angles of 0º and 60º, 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 =0.075N/m, density of water =1000kg/ $m^{3}$ , take g=10m/ $s^{2}$ ]

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a

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

b

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

c

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.

d

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

answer is A.

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Detailed Solution

$h = \frac{2 T \cos α}{ρ g r}$

$α_{1} = 0^{\circ} α_{2} = 60^{\circ}$

$h_{1} = \frac{2 \times 0.075 \cos 0^{\circ}}{(0.2) \times 10^{- 3} \times 10^{3} \times 10} = 0.075 m = 7.5 cm$

$h_{2} = \frac{2 \times 0.075 \times \cos 60 º}{0.2 \times 10^{- 3} \times 10^{3} \times 10} = 3.75 cm$

$Case 1 : If point is 5 cm above (5 c m < 7.5 cm)$

$The contact angle or radius of curvature of meniscus will adjust itself for 5 cm height.$

$C ase 2 : 5 cm > 3.75 cm$

$h = 3.75 cm$

Weight of water in meniscus will be different in two cases because angle of contact is different .

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