Question

The energy stored in a soap bubble of diameter 4 cm is nearly (surface tension of soap solution is 0.07 N/m)

• A. $8.5 \times 10^{-3}$ J
• B. $2.75 \times 10^{-2}$ J
• C. $7 \times 10^{-4}$ J
• D. $4.5 \times 10^{-4}$ J
• E. $3.15 \times 10^{-3}$ J

Hint:

A soap bubble has two surfaces, so the energy stored must account for both.

Answer 1

The Correct Option is C

Step 1: The energy stored in a soap bubble due to surface tension is given by:

U = 4 π R² × 2T

where T is the surface tension, and the factor of 2 is included because a soap bubble has both an inner and outer surface.

Step 2: Given:

Diameter = 4 cm = 0.04 m, R = 0.02 m

T = 0.07 N/m

Step 3: Substituting the values:

U = 4 π (0.02)² × 2 (0.07)

Step 4: Simplifying:

U = 4 × 3.1416 × 0.0004 × 0.14

U = 7 × 10⁻⁴ J

Step 5: Therefore, the correct answer is (C).