Import Question JSON

Current Question (ID: 19226)

Question:

$\text{Two particles } A \text{ and } B \text{ of equal mass } M \text{ are moving with the same speed } v \text{ as shown in the figure.}$ $\text{They collide completely inelastically and move as a single particle } C. \text{ The angle } \theta \text{ that the path of } C \text{ makes with the } x\text{-axis is given by:}$

Options:

1. $\tan \theta = \frac{\sqrt{3} + \sqrt{2}}{1 - \sqrt{2}}$
2. $\tan \theta = \frac{1 - \sqrt{3}}{1 + \sqrt{2}}$
3. $\tan \theta = \frac{\sqrt{3} - \sqrt{2}}{1 - \sqrt{2}}$
4. $\tan \theta = \frac{1 - \sqrt{3}}{\sqrt{2}(1 + \sqrt{3})}$

Solution:

$\text{Hint: Use the conservation of linear momentum.}$

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
}