Import Question JSON

Current Question (ID: 16503)

Question:

$\text{On rotating a point charge having a charge } q \text{ around a charge } Q \text{ in a circle of radius } r, \text{ the work done will be:}$

Options:

1. $q \times 2\pi r$
2. $\frac{q \times 2\pi Q}{r}$
3. $\text{zero}$
4. $\frac{Q}{2\varepsilon_0 r}$

Solution:

$\text{Hint: } W = q \Delta V$ $\text{Explanation: The equipotential surface is a surface with a constant value of potential at all points on the surface.}$ $\text{Since charge } q \text{ moving on an equipotential surface, therefore, work done is zero.}$ $\Rightarrow W = 0$ $\text{Hence, option (3) is the correct answer.}$

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
}