First slide

Surface tension and surface energy

Question

A loop of 6.28 cm long thread is put gently on a soap film in a wire loop. The film is pricked with a needle inside the soap film enclosed by the thread. If the surface tension of soap solution is 0.030 N/m, then the tension in the thread is

Moderate

A

$1 \times 10^{- 4} N$
B

$2 \times 10^{- 4} N$
C

$3 \times 10^{- 4} N$
D

$4 \times 10^{- 4} N$

Solution

When the soap film enclosed by the thread is pricked, the thread would take up a circular shape. Consider a small element of the thread. While horizontal components of tension get balanced, the vertical components get added up.
$\begin{array}{l} 2 Tsin θ = σΔl \\ 2 Tθ = σ (2 θ \times r) \\ \begin{aligned} T = σr = σ \times \frac{2 πr}{2 π} & = 0 .030 \times \frac{6 .28 \times 10^{- 2}}{2 π} N \\ = 3 \times 10^{- 4} N \end{aligned} \end{array}$

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