A thin liquid film formed between a U-shaped wire and a light slider supports a weight of $1.5 \times 10^{-2} \mathrm{~N}$ (see figure). The length of the slider is $30 \mathrm{~cm}$ and its weight negligible. The surface tension of the liquid film is

• A

  $0.0125 \mathrm{~Nm}^{-1}$
• B

  $0.1 \mathrm{~Nm}^{-1}$
• C

  $0.05 \mathrm{~Nm}^{-1}$
• Correct answer
  D

  $0.025 \mathrm{~Nm}^{-1}$

Solution

The force of surface tension acting on the slider balances the force due to the weight. $\begin{array}{ll} \Rightarrow & \mathrm{F}=2 \mathrm{~T} \ell=\mathrm{w} \\ \Rightarrow & 2 \mathrm{~T}(0.3)=1.5 \times 10^{-2} \\ \Rightarrow & \mathrm{T}=2.5 \times 10^{-2} \mathrm{~N} / \mathrm{m} \end{array}$

Hence, the correct answer is option: 'D'.