Question

If the diameter of droplet and surface tension of water are 0.05 mm and 0.075 N/m respectively, then the pressure inside of droplet in excess of the outside pressure intensity is

• A. 3 kN/m$^2$
• B. 6 kN/m$^2$
• C. $3 \times 10^3$ kN/m$^2$
• D. $6 \times 10^3$ kN/m$^2$

Hint:

Remember the different formulas for excess pressure due to surface tension:
- Liquid Droplet: $\Delta P = 4\sigma/d$
- Hollow Bubble (like a soap bubble): $\Delta P = 8\sigma/d$
- Liquid Jet: $\Delta P = 2\sigma/d$
A common mistake is using the wrong formula.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
Water droplet d=0.05mm, σ=0.075 N/m. Find excess pressure.

Step 2: Key Formula (Alternate):
ΔP = 4σ/d (liquid droplet). Bubble: 8σ/d. Jet: 2σ/d. One curved surface for droplet.

Step 3: Detailed Explanation:
ΔP = 4×0.075/(0.05×10⁻³) = 0.3/5×10⁻⁵ = 6000 N/m² = 6 kN/m². Smaller droplet → higher internal pressure.

Step 4: Final Answer:
6 kN/m².