Import Question JSON

Current Question (ID: 20186)

Question:

$\text{Two uniformly charged spherical conductors } A \text{ and } B \text{ of radii } 5 \text{ mm and } 10 \text{ mm are separated by a distance of } 2 \text{ cm.}$ $\text{If the spheres are connected by a conducting wire, then in equilibrium condition,}$ $\text{the ratio of the magnitudes of the electric fields at the surface of the sphere } A \text{ and } B \text{ will be:}$

Options:

1. $1 : 2$
2. $2 : 1$
3. $1 : 1$
4. $1 : 4$

Solution:

$\text{Hint: } E = \frac{kQ}{r^2}$

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
}