Import Question JSON

Current Question (ID: 9567)

Question:

$\text{Two particles move from A to C and A to D on a circle of radius R and the diameter AB. If the time taken by both particles is the same, then the ratio of magnitudes of their average velocities is:}$

Options:

1. $2$
2. $2\sqrt{3}$
3. $\sqrt{3}$
4. $\frac{\sqrt{3}}{2}$

Solution:

$\text{Hint: Recall the average velocity.}$ $\text{Step: Find the ratio of magnitudes of their average velocities.}$ $\text{From the figure:}$ $AC = 2R \cos 30° = \sqrt{3}R$ $AD = 2R \cos 60° = R$ $\text{As } t_1 = t_2\text{,}$ $\Rightarrow \frac{\sqrt{3}R}{v_1} = \frac{R}{v_2} \Rightarrow \frac{v_1}{v_2} = \sqrt{3}$ $\text{Hence, option (3) is the correct answer.}$

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
}