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MHT CET · Physics · Mechanical Properties of Fluids

Three liquids have same surface tension and densities \(\varrho_{1}, Q_{2}\), and \(\varrho_{3}\left(\varrho_{1}>\varrho_{2}>\varrho_{3}\right)\).
In three identical capillaries, rise of liquid is same. The corresponding angles of contact \(\theta_{1}, \theta_{2}\) and \(\theta_{3}\) are related as

  1. A \(\theta_{1}>\theta_{2}>\theta_{3}\)
  2. B \(\theta_{1} < \theta_{2}>\theta_{3}\)
  3. C \(\theta_{1}>\theta_{2} < \theta_{3}\)
  4. D \(\theta_{1} < \theta_{2} < \theta_{3}\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(\theta_{1} < \theta_{2} < \theta_{3}\)

Step-by-step Solution

Detailed explanation

Rise of a liquid in a capillary tube is given by,
\(\mathrm{h}=\frac{2 \mathrm{T} \cos \theta}{\mathrm{r} \rho \mathrm{g}}\)
or \(\cos \theta=h r \rho g / 2 T\)
where \(\theta=\) angle of contact,
\(\mathrm{r}=\) radius of capillary tube
\(\mathrm{T}=\) surface tension
\(\rho=\) density of liquid
now given that \(h\), \(T\) and \(r\) are constants for all three liquids,
and \(\rho_{1}>\rho_{2}>\rho_{3}\),
therefore \(\cos \theta_{1}>\cos \theta_{2}>\cos \theta_{3}\)
or \(\theta_{1} < \theta_{2} < \theta_{3}\)
now as the liquid is rising in all three capillaries therefore angles of contact will be acute,
\(0 \leq \theta_{1} < \theta_{2} < \theta_{3} < \frac{\pi}{2}\)
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