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If a capillary of diameter 4 × 10-6 m is used, determine the capillary rise in water (σw = 0.07N/m, g = 10 m/s2).
- a)70 cm
- b)7 m
- c)70 m
- d)0.7 m
Correct answer is option 'B'. Can you explain this answer?
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Given data:
Diameter of capillary (d) = 4 × 10^-6 m
Surface tension of water (σw) = 0.07 N/m
Acceleration due to gravity (g) = 10 m/s^2
Formula used:
The capillary rise (h) in a capillary tube is given by the formula:
h = (2σw cosθ) / (ρgR)
Where:
σw = Surface tension of the liquid
θ = Contact angle
ρ = Density of the liquid
g = Acceleration due to gravity
R = Radius of the capillary tube
Calculation:
Given that the diameter of the capillary tube is 4 × 10^-6 m, we can find the radius (R) using the formula:
R = d/2 = 4 × 10^-6 m / 2 = 2 × 10^-6 m
Substitute the values into the formula:
h = (2 * 0.07 * 1) / (1000 * 10 * 2 × 10^-6)
h = 0.14 / 0.02
h = 7 m
Therefore, the capillary rise in water when a capillary of diameter 4 × 10^-6 m is used is 7 meters. Hence, option (b) is correct.
Diameter of capillary (d) = 4 × 10^-6 m
Surface tension of water (σw) = 0.07 N/m
Acceleration due to gravity (g) = 10 m/s^2
Formula used:
The capillary rise (h) in a capillary tube is given by the formula:
h = (2σw cosθ) / (ρgR)
Where:
σw = Surface tension of the liquid
θ = Contact angle
ρ = Density of the liquid
g = Acceleration due to gravity
R = Radius of the capillary tube
Calculation:
Given that the diameter of the capillary tube is 4 × 10^-6 m, we can find the radius (R) using the formula:
R = d/2 = 4 × 10^-6 m / 2 = 2 × 10^-6 m
Substitute the values into the formula:
h = (2 * 0.07 * 1) / (1000 * 10 * 2 × 10^-6)
h = 0.14 / 0.02
h = 7 m
Therefore, the capillary rise in water when a capillary of diameter 4 × 10^-6 m is used is 7 meters. Hence, option (b) is correct.
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