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Water rises in a capillary tube upto a height of 10cm whereas mercury depresses in it by 3.42cm.If the angle of contact is 135 degree and density of mercury is 13.6gm/cc.Then the ratio of the surface tension of water and mercury will be nearly?
Verified Answer
Water rises in a capillary tube upto a height of 10cm whereas mercury ...
Let a liquid of density ρ rise a height h in a capillary of radius r
And we can suppose:
hrρg = 2Tcosθ
Where T is surface tension of that liquid and θ is angle of contact and
θw is the angle of contact of water
Let Tm and Tw be the surface tension of water and mercury.
Tm/Tw = [(3.112 * 13.6)/(10 * 1)] * [cosθw / cos(1350)]
= 5.98*cosθw
This question is part of UPSC exam. View all NEET courses
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Water rises in a capillary tube upto a height of 10cm whereas mercury ...
Calculating the ratio of surface tension of water to mercury
- Given data:
- Height of water rise (h1) = 10 cm
- Height of mercury depression (h2) = 3.42 cm
- Angle of contact (θ) = 135 degrees
- Density of mercury (ρ) = 13.6 g/cm^3
Calculating surface tension of water
The height of rise in a capillary tube is given by the formula:
\[ h = \frac{2T \cos \theta}{\rho g r} \]
where:
- T is the surface tension
- θ is the angle of contact
- ρ is the density of the liquid
- g is the acceleration due to gravity
- r is the radius of the capillary tube
Substitute the given values for water:
\[ 10 = \frac{2T \cos 135}{1 \times 10 \times r} \]
\[ 10 = \frac{-2T}{10r} \]
\[ T = -5r \]
Calculating surface tension of mercury
For mercury, the formula becomes:
\[ h = \frac{2T \cos \theta}{\rho g r} \]
Substitute the given values for mercury:
\[ -3.42 = \frac{2T \cos 135}{13.6 \times 10 \times r} \]
\[ -3.42 = \frac{-2T}{136r} \]
\[ T = 68r \]
Calculating the ratio of surface tension
Now, we have:
\[ \frac{T_{water}}{T_{mercury}} = \frac{-5r}{68r} = -\frac{5}{68} \]
Therefore, the ratio of the surface tension of water to mercury is approximately \(\frac{5}{68}\).
- Given data:
- Height of water rise (h1) = 10 cm
- Height of mercury depression (h2) = 3.42 cm
- Angle of contact (θ) = 135 degrees
- Density of mercury (ρ) = 13.6 g/cm^3
Calculating surface tension of water
The height of rise in a capillary tube is given by the formula:
\[ h = \frac{2T \cos \theta}{\rho g r} \]
where:
- T is the surface tension
- θ is the angle of contact
- ρ is the density of the liquid
- g is the acceleration due to gravity
- r is the radius of the capillary tube
Substitute the given values for water:
\[ 10 = \frac{2T \cos 135}{1 \times 10 \times r} \]
\[ 10 = \frac{-2T}{10r} \]
\[ T = -5r \]
Calculating surface tension of mercury
For mercury, the formula becomes:
\[ h = \frac{2T \cos \theta}{\rho g r} \]
Substitute the given values for mercury:
\[ -3.42 = \frac{2T \cos 135}{13.6 \times 10 \times r} \]
\[ -3.42 = \frac{-2T}{136r} \]
\[ T = 68r \]
Calculating the ratio of surface tension
Now, we have:
\[ \frac{T_{water}}{T_{mercury}} = \frac{-5r}{68r} = -\frac{5}{68} \]
Therefore, the ratio of the surface tension of water to mercury is approximately \(\frac{5}{68}\).
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Water rises in a capillary tube upto a height of 10cm whereas mercury depresses in it by 3.42cm.If the angle of contact is 135 degree and density of mercury is 13.6gm/cc.Then the ratio of the surface tension of water and mercury will be nearly?
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Water rises in a capillary tube upto a height of 10cm whereas mercury depresses in it by 3.42cm.If the angle of contact is 135 degree and density of mercury is 13.6gm/cc.Then the ratio of the surface tension of water and mercury will be nearly? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Water rises in a capillary tube upto a height of 10cm whereas mercury depresses in it by 3.42cm.If the angle of contact is 135 degree and density of mercury is 13.6gm/cc.Then the ratio of the surface tension of water and mercury will be nearly? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Water rises in a capillary tube upto a height of 10cm whereas mercury depresses in it by 3.42cm.If the angle of contact is 135 degree and density of mercury is 13.6gm/cc.Then the ratio of the surface tension of water and mercury will be nearly?.
Water rises in a capillary tube upto a height of 10cm whereas mercury depresses in it by 3.42cm.If the angle of contact is 135 degree and density of mercury is 13.6gm/cc.Then the ratio of the surface tension of water and mercury will be nearly? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Water rises in a capillary tube upto a height of 10cm whereas mercury depresses in it by 3.42cm.If the angle of contact is 135 degree and density of mercury is 13.6gm/cc.Then the ratio of the surface tension of water and mercury will be nearly? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Water rises in a capillary tube upto a height of 10cm whereas mercury depresses in it by 3.42cm.If the angle of contact is 135 degree and density of mercury is 13.6gm/cc.Then the ratio of the surface tension of water and mercury will be nearly?.
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