Question 16 of 18intermediate🔧 ApplyNumerical3 marks

A U-shaped wire is dipped in a soap solution, and removed. The thin soap film formed between the wire and the light slider supports a weight of 1.5×101.5 \times 10⁻² N (which includes the small weight of the slider). The length of the slider is 30 cm. What is the surface tension of the film?

Correct Answer

The surface tension of the soap film is 2.5×102.5 \times 10⁻² N/m.

Exercise: EXERCISES | Q: 9.17 | (Page 22)
For More Understanding

Explanation

This question tests understanding of surface tension in soap films. The key concept from the textbook is that a soap film has TWO surfaces (front and back), unlike a single liquid-air interface. The context clearly shows that for a film, S = F/2l, where the factor of 2 accounts for both surfaces. The weight supported by the film is balanced by the surface tension force from both surfaces acting along the length of the slider.

Solution Steps

  1. Given: Weight supported (F) = 1.5×101.5 \times 10⁻² N; Length of slider (l) = 30 cm = 0.30 m

  2. Principle: A soap film has two surfaces. The force due to surface tension acts along both surfaces of the film.

  3. Formula: From the context, for a film with two surfaces: Surface tension S = F/(2l)

  4. Calculation: S = (1.5×101.5 \times 10⁻²)/(2×0.302 \times 0.30) = (1.5×101.5 \times 10⁻²)/0.60 = 2.5×102.5 \times 10⁻² N/m

  5. Answer: The surface tension of the soap film is 2.5×102.5 \times 10⁻² N/m.

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