A cylindrical capillary tube of 0.2 mm radius is made by joining two capillaries T₁ and T₂ of different materials having water contact angles of 0⁰ and 60⁰ , 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 a water = 0.075 N/m, density of water = 1000 kg/m³ , take g = 10 m/s² ]
A. 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)
B. 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 the water in the meniscus)
C. 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 the water in the meniscus)
D. 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.
Answers
A cylindrical capillary tube of 0.2 mm radius is made by joining two capillaries T₁ and T₂ of different materials having water contact angles of 0⁰ and 60⁰ , 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 a water = 0.075 N/m, density of water = 1000 kg/m³ , take g = 10 m/s² ]
A. 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)
B. 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 the water in the meniscus)
C. 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 the water in the meniscus)
D. 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.
Explanation:
The correct options are
A,B and D
(2*0.075*1/10³ *10*2*10⁻⁴*2)*100cm
=3.75
Option A is correct
2T CosФ / ρgr
For C angle of contact will adjust to make h=5
The shape of meniscus is different in the two cases
Explanation:
Given
A cylindrical capillary tube of 0.2 mm radius is made by joining two capillaries T₁ and T₂ of different materials having water contact angles of 0⁰ and 60⁰ , 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 a water = 0.075 N/m, density of water = 1000 kg/m³ , take g = 10 m/s² ]
A. 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)
B. 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 the water in the meniscus)
C. 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 the water in the meniscus)
D. 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.
- First let us find the height .
- So h is given by h = 2T cos theta / R ρ g
- = 2 x 7.5 x 10^-2 cos 60 / 0.2x 10^-3 x 10^2 x 9.8
- = 15 x 10^-2 x 1/2 / 1.96 x 10^-1
- = 7.5 / 2 x 10^-2
- = 3.75 x 10^-2 m
- = 3.75 cm
- Now when T1 is in contact with water then h = 7.5 cm which is less than 8 cm
- Also when T2 is in contact with water then h = 3.5 cm which is less than 5 cm
- Volume of water in the meniscus depends upon the angle of contact.
- Therefore option A, C, D holds good.
Reference link will be
https://brainly.in/question/6994318