Question 23: The amount of energy required to form a soap bubble of radius 2 cm from a soap solution is nearly : (surface tension of soap solution =0.03 \mathrm{~N} \mathrm{~m}^{-1} )
(1) 3.01 \times 10^{-4} \mathrm{~J}
(2) 50.1 \times 10^{-4} \mathrm{~J}
(3) 30.16 \times 10^{-4} \mathrm{~J}
(4) 5.06 \times 10^{-4} \mathrm{~J}
Answer: Option (1)
Explanation:
A soap bubble has two surfaces, inner and outer.
Therefore, the energy required to form a soap bubble is equal to the surface energy of both surfaces.
Surface energy is given by
E = 2 \times 4\pi r^{2} \times Twhere r is the radius of the bubble and T is the surface tension.
Given radius,
r = 2 \, \mathrm{cm} = 0.02 \, \mathrm{m}Surface tension,
T = 0.03 \, \mathrm{N\,m^{-1}}Substituting the values,
E = 2 \times 4\pi \times (0.02)^{2} \times 0.03 E = 8\pi \times 0.0004 \times 0.03 E \approx 3.01 \times 10^{-4} \, \mathrm{J}Hence, the energy required to form the soap bubble is nearly 3.01 \times 10^{-4} \, \mathrm{J}.
Therefore, the correct answer is Option (1).