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Chapter 8: Problem 82

Surface tension of the soap solution is (A) \(\frac{m g}{4 \ell \tan \frac{\theta}{2}}\) (B) \(\frac{m g}{2 \ell \tan \frac{\theta}{2}}\) (C) \(\frac{m g}{4 \ell \tan \theta}\) (D) None of these

Short Answer

Expert verified
The correct expression for the surface tension of the soap solution is none of the given options, so the answer is (D) None of these.

Step by step solution

01

Identifying the surface tension formula for a liquid film

The surface tension of a liquid film is given by the formula T = mgL, where T is the surface tension, m is the mass of the object, g is the acceleration due to gravity, and L is the length of the soap film. We will derive the correct expression for the surface tension by finding the right relationship between these parameters and the options given in the problem.
02

Analyzing and eliminating incorrect options

Let's analyze the given options and eliminate the ones that do not match the surface tension formula T = mgL: (A) \(\frac{m g}{4 \ell \tan \frac{\theta}{2}}\): This option has an extra term with the tangent of half the angle, which is not present in the formula T = mgL. Eliminate this option. (B) \(\frac{m g}{2 \ell \tan \frac{\theta}{2}}\): Similar to option (A), this option also has an extra term with the tangent of half the angle, which is not in the formula T = mgL. Eliminate this option as well. (C) \(\frac{m g}{4 \ell \tan \theta}\): This option includes a term with the tangent of the angle 胃. This term is not present in the surface tension formula T = mgL, so we eliminate this option. (D) None of these: Since none of the given options match the surface tension formula T = mgL, we select option (D) as the correct answer.

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