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What will be the diameter (in mm) of a water droplet, the pressure inside which is 0.05 N/cm2 greater than the outside pressure? (Take surface tension as 0.075 N/m)
- a)3
- b)0.3
- c)0.6
- d)6
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
What will be the diameter (in mm) of a water droplet, the pressure ins...
Explanation: p = 4σ/d
where p = pressure difference between the liquid droplet and the surrounding medium, σ = surface tension and d = diameter of the droplet. Substituting all the values,
where p = pressure difference between the liquid droplet and the surrounding medium, σ = surface tension and d = diameter of the droplet. Substituting all the values,
This question is part of UPSC exam. View all Civil Engineering (CE) courses
Most Upvoted Answer
What will be the diameter (in mm) of a water droplet, the pressure ins...
To determine the diameter of the water droplet, we need to consider the pressure difference between the inside and outside of the droplet and the surface tension of water.
Given:
Inside pressure - outside pressure = 0.05 N/cm^2
Surface tension of water (σ) = 0.075 N/m
Let's assume the diameter of the water droplet as 'D.'
Step 1: Convert the pressure difference from N/cm^2 to N/m^2.
Inside pressure - outside pressure = 0.05 N/cm^2 = 0.05 x 10^4 N/m^2 (since 1 N/cm^2 = 10^4 N/m^2)
Step 2: Calculate the excess pressure inside the droplet.
Excess pressure = Inside pressure - outside pressure = 0.05 x 10^4 N/m^2
Step 3: Determine the excess pressure due to surface tension.
Excess pressure = 2σ / D
Step 4: Equate the excess pressures from steps 2 and 3.
0.05 x 10^4 = 2 x 0.075 / D
Step 5: Solve for D.
D = 2 x 0.075 / (0.05 x 10^4)
= 2 x 0.075 / 0.5 x 10^3
= 0.15 / 0.5 x 10^3
= 0.15 x 10^-3 / 0.5
= 0.3 x 10^-3
= 0.3 mm
Therefore, the diameter of the water droplet is 0.3 mm, which corresponds to option 'C'.
Given:
Inside pressure - outside pressure = 0.05 N/cm^2
Surface tension of water (σ) = 0.075 N/m
Let's assume the diameter of the water droplet as 'D.'
Step 1: Convert the pressure difference from N/cm^2 to N/m^2.
Inside pressure - outside pressure = 0.05 N/cm^2 = 0.05 x 10^4 N/m^2 (since 1 N/cm^2 = 10^4 N/m^2)
Step 2: Calculate the excess pressure inside the droplet.
Excess pressure = Inside pressure - outside pressure = 0.05 x 10^4 N/m^2
Step 3: Determine the excess pressure due to surface tension.
Excess pressure = 2σ / D
Step 4: Equate the excess pressures from steps 2 and 3.
0.05 x 10^4 = 2 x 0.075 / D
Step 5: Solve for D.
D = 2 x 0.075 / (0.05 x 10^4)
= 2 x 0.075 / 0.5 x 10^3
= 0.15 / 0.5 x 10^3
= 0.15 x 10^-3 / 0.5
= 0.3 x 10^-3
= 0.3 mm
Therefore, the diameter of the water droplet is 0.3 mm, which corresponds to option 'C'.
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