Introduction

Understanding internal pressure in a spherical water droplet at sea level is crucial for mastering surface tension and Laplace pressure concepts in competitive physics exams.

Due to surface tension, the pressure inside a tiny droplet becomes higher than the surrounding atmospheric pressure, and this excess pressure is directly related to the surface tension and radius of the droplet.

This MCQ tests whether you correctly link internal pressure, atmospheric pressure, and surface tension in a real-world situation like a water droplet at sea level.

Core Concept: Pressure Inside a Droplet

For a spherical liquid droplet (like a water droplet in air), the excess internal pressure over the outside pressure is given by the Laplace pressure formula:

ΔP = P_inside − P_outside = 2T / r

Here, T is the surface tension of the liquid and r is the radius of the droplet.

At sea level, the outside pressure P_outside is atmospheric pressure, so the internal pressure becomes P_inside = P_atm + 2T / r, clearly greater than atmospheric pressure and dependent on surface tension.

Option-by-Option Analysis

Option (a)

Statement: lower than atmospheric pressure, and depends on surface tension

For a droplet, surface tension pulls the surface inward, which must be balanced by a higher pressure inside than outside; mathematically ΔP = 2T / r > 0, so P_inside > P_outside, not lower.

Although this option correctly mentions “depends on surface tension,” it is wrong because it claims the internal pressure is lower than atmospheric pressure.

Option (b)

Statement: lower than atmospheric pressure, and independent of surface tension

This is incorrect in both parts: the internal pressure in a spherical water droplet is higher than the external atmospheric pressure, and the excess pressure is directly proportional to surface tension T.

If surface tension were zero, a finite droplet shape would not be stable and there would be no excess internal pressure, showing that surface tension is essential.

Option (c) – Correct

Statement: higher than atmospheric pressure, and depends on surface tension

Using P_inside = P_atm + 2T / r, the internal pressure must exceed atmospheric pressure at sea level by an amount 2T / r.

This excess pressure clearly depends on surface tension T (and radius r), so this option matches both the sign (higher than atmospheric) and the dependence on surface tension, making it the correct answer.

Option (d)

Statement: higher than atmospheric pressure, and independent of surface tension

This option gets the sign right (inside pressure is higher than atmospheric) but ignores the physical cause, which is surface tension.

Removing surface tension (T = 0) would make the excess pressure 2T / r = 0, so the internal pressure would just equal atmospheric pressure, proving that the internal pressure is not independent of surface tension.