Properties of Matter 4 Question 15
17. A container of width $2 a$ is filled with a liquid. A thin wire of weight per unit length $\lambda$ is gently placed over the liquid surface in the middle of the surface as shown in the figure. As a result, the liquid surface is depressed by a distance $y(y«a)$. Determine the surface tension of the liquid.
(2004, 2M)
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Answer:
Correct Answer: 17. $\frac{\lambda a}{2 y}$
Solution:
- Free body diagram of the wire is as shown in figure.
Considering the equilibrium of wire in vertical direction, we have
$$ 2 T l \cos \theta=\lambda l g \cdots(i) $$
$$ \text { For } \quad y«a, \cos \theta \approx \frac{y}{a} $$
Substituting the values in Eq. (i), we get
$$ T=\frac{\lambda a}{2 y} $$
