Import Question JSON

Current Question (ID: 20110)

Question:

$\text{A positive point charge is released from rest at a distance } r_0 \text{ from a position line charge with uniform density.}$ $\text{The speed } (v) \text{ of the point charge, as a function of instantaneous distance } r \text{ from line charge, is proportional to:}$

Options:

1. $v \propto e^{+r/r_0}$
2. $v \propto \ln\left(\frac{r}{r_0}\right)$
3. $v \propto \left(\frac{r}{r_0}\right)$
4. $v \propto \sqrt{\ln\left(\frac{r}{r_0}\right)}$

Solution:

$\text{Hint: } \vec{E} = -\frac{dV}{dr}$ $E \propto \frac{1}{r}$ $\Delta V \propto \ln\left(\frac{r}{r_0}\right)$ $\frac{1}{2}mv^2 \propto \ln\left(\frac{r}{r_0}\right)$ $v \propto \sqrt{\ln\left(\frac{r}{r_0}\right)}$

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
}