COMEDK · Physics · 11. Mechanical Properties of Fluids
What is the relation obeyed by the angles of contact \(\theta_1, \theta_2\) and \(\theta_3\) of 3 liquids of different densities \(P_1, P_2\) and \(P_3\) respectively \((\mathrm{P}_1 < \mathrm{P}_2 < \mathrm{P}_3\)) when they rise to the same capillary height in 3 identical capillaries and having nearly same surface tension \(\mathrm{T}\) ?
- A \(\pi > \theta_1 > \theta_2 > \theta_3 \ge \dfrac{\pi}{2}\)
- B \(0 \le \theta_1 < \theta_2 < \theta_3 < \dfrac{\pi}{2}\)
- C \(\dfrac{\pi}{2} < \theta_1 < \theta_2 < \theta_3 \le \pi\)
- D \(\dfrac{\pi}{2} > \theta_1 > \theta_2 > \theta_3 \ge 0\)
Answer & Solution
Correct Answer
(D) \(\dfrac{\pi}{2} > \theta_1 > \theta_2 > \theta_3 \ge 0\)
Step-by-step Solution
Detailed explanation
From Jurin's law: \(h = \dfrac{2T\cos\theta}{rPg}\) Since \(h\), \(T\), \(r\), \(g\) are constant: \(\cos\theta \propto P\) Given \(P_1 0\)), \(\cos\theta > 0\), so all angles are acute: \(0 \leq \theta \theta_2 > \theta_3\) Combined:…
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