Import Question JSON

Current Question (ID: 10510)

Question:

$\text{Three liquids of densities } \rho_1, \rho_2 \text{ and } \rho_3 \text{ (with } \rho_1 > \rho_2 > \rho_3\text{), having the same value of surface tension } T\text{, rise to the same height in three identical capillaries. The angles of contact } \theta_1, \theta_2 \text{ and } \theta_3 \text{ obey:}$

Options:

1. $\frac{\pi}{2} > \theta_1 > \theta_2 > \theta_3 \geq 0$
2. $0 \leq \theta_1 < \theta_2 < \theta_3 < \frac{\pi}{2}$
3. $\frac{\pi}{2} < \theta_1 < \theta_2 < \theta_3 < \pi$
4. $\pi > \theta_1 > \theta_2 > \theta_3 > \frac{\pi}{2}$

Solution:

$\text{According to ascent formula for capillary tube,}$ $h = \frac{2T \cos \theta}{\rho gr}$ $\therefore \frac{\cos \theta_1}{\rho_1} = \frac{\cos \theta_2}{\rho_2} = \frac{\cos \theta_3}{\rho_3}$ $\text{Thus, } \cos \theta \propto \rho$ $\therefore \rho_1 > \rho_2 > \rho_3$ $\therefore \cos \theta_1 > \cos \theta_2 > \cos \theta_3$ $0 \leq \theta_1 < \theta_2 < \theta_3 < \frac{\pi}{2}$

Import JSON File

Upload a JSON file containing LaTeX/MathJax formatted question, options, and solution.

Expected JSON Format:

{
  "question": "The mass of carbon present in 0.5 mole of $\\mathrm{K}_4[\\mathrm{Fe(CN)}_6]$ is:",
  "options": [
    {
      "id": 1,
      "text": "1.8 g"
    },
    {
      "id": 2,
      "text": "18 g"
    },
    {
      "id": 3,
      "text": "3.6 g"
    },
    {
      "id": 4,
      "text": "36 g"
    }
  ],
  "solution": "\\begin{align}\n&\\text{Hint: Mole concept}\\\\\n&1 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\text{ moles of carbon atom}\\\\\n&0.5 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\times 0.5 \\text{ mol} = 3 \\text{ mol}\\\\\n&1 \\text{ mol of carbon} = 12 \\text{ g}\\\\\n&3 \\text{ mol carbon} = 12 \\times 3 = 36 \\text{ g}\\\\\n&\\text{Hence, 36 g mass of carbon present in 0.5 mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6].\n\\end{align}",
  "correct_answer": 4
}