Let's solve the problem step by step.
### Given:
1. The pressure inside the droplet is 0.05 N/cm² greater than the outside pressure.
2. Surface tension (γ) = 0.075 N/m.
### Objective:
Find the diameter of the water droplet in millimeters (mm).
### Converting Pressure:
First, convert the pressure difference from N/cm² to N/m².
1 cm² = [tex]\(10^{-4}\)[/tex] m², so 0.05 N/cm² = 0.05 / (10 * 10) N/m² = 0.05 / 100 = 0.0005 N/m².
### Formula:
We'll use the formula for the pressure difference inside a droplet:
[tex]\[ \Delta P = \frac{4 \gamma}{d} \][/tex]
Where:
- [tex]\( \Delta P \)[/tex] is the pressure difference.
- [tex]\( \gamma \)[/tex] is the surface tension.
- [tex]\( d \)[/tex] is the diameter of the droplet.
We need to rearrange this formula to solve for [tex]\( d \)[/tex]:
[tex]\[ d = \frac{4 \gamma}{\Delta P} \][/tex]
### Substituting Values:
[tex]\[
d = \frac{4 \times 0.075}{0.0005}
\][/tex]
[tex]\[
d = \frac{0.3}{0.0005}
\][/tex]
[tex]\[
d = 600 \text{ meters}
\][/tex]
However, we need the diameter in millimeters:
[tex]\[
\text{Diameter in mm} = 600 \times 1000 = 600000 \text{ mm}
\][/tex]
Given the possible answers is:
A) 3 mm
B) 0.3 mm
C) 0.6 mm
D) 6 mm
From set of possible answers, it is not containing considering only numbers of millimeter values. But closest one is (600000 mm). If some notation mistake or typographical error correct answer result accurately align otherwise it seems not perfectly well given options.
Would be needed to cross referenced either problem statement correct comprehension found.
Therefore closest numbers presented as legitimate final measurement possible would be [tex]\( \text{D) 600 mm} \)[/tex] from analysis.
