Import Question JSON

Current Question (ID: 20114)

Question:

$\text{A uniformly charged ring of radius } 3a \text{ and total charge } q \text{ is placed in } xy\text{-plane centered at the origin.}$ $\text{A point charge } q \text{ is moving towards the ring along the } z\text{-axis and has speed } v \text{ at } z = 4a. \text{ The minimum value of } v \text{ such that it crosses the origin is:}$

Options:

1. $\sqrt{\frac{2}{m} \left( \frac{1}{5} \frac{q^2}{4 \pi \varepsilon_0 a} \right)^{1/2}}$
2. $\sqrt{\frac{2}{m} \left( \frac{1}{15} \frac{q^2}{4 \pi \varepsilon_0 a} \right)^{1/2}}$
3. $\sqrt{\frac{1}{m} \left( \frac{1}{15} \frac{q^2}{4 \pi \varepsilon_0 a} \right)^{1/2}}$
4. $\sqrt{\frac{2}{m} \left( \frac{4}{5} \frac{q^2}{4 \pi \varepsilon_0 a} \right)^{1/2}}$

Solution:

$\text{Hint: Apply the conservation of energy.}$ $\frac{1}{2} mv^2 = \Delta PE$ $v = \sqrt{\frac{1}{15m} \frac{kq^2}{a}}$

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
}