Import Question JSON

Current Question (ID: 20123)

Question:

$\text{Two isolated conducting spheres } S_1 \text{ and } S_2 \text{ of radius } \frac{2R}{3} \text{ and } \frac{R}{3} \text{ have } 12 \, \mu\text{C} \text{ and } -3 \, \mu\text{C} \text{ charges, respectively, and are at a large distance from each other. They are now connected by a conducting wire. A long time after this is done the charges on } S_1 \text{ and } S_2 \text{ are respectively,}$

Options:

1. $6 \, \mu\text{C} \text{ and } 3 \, \mu\text{C}$
2. $4.5 \, \mu\text{C} \text{ on both}$
3. $3 \, \mu\text{C} \text{ and } 6 \, \mu\text{C}$
4. $+4.5 \, \mu\text{C} \text{ and } -4.5 \, \mu\text{C}$

Solution:

$\text{Hint: The charge is conserved. } V = \frac{KQ}{R}. $ $\text{Now,}$ $Q_1 + Q_2 = Q'_1 + Q'_2 = 12 \, \mu\text{C} - 3 \, \mu\text{C} = 9 \, \mu\text{C}$ $\text{and } V_1 = V_2 = \frac{KQ'_1}{\frac{2R}{3}} = \frac{KQ'_2}{\frac{R}{3}}$ $Q'_1 = 2Q'_2 = 2Q'_2 + Q'_2 = 9 \, \mu\text{C}$ $\text{and } Q'_2 = 3 \, \mu\text{C}$ $\text{and } Q'_1 = 6 \, \mu\text{C}$

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
}