Import Question JSON

Current Question (ID: 20198)

Question:

$\text{Two charged conducting spheres of radii } a \text{ and } b \text{ are connected to each other by a conducting wire. The ratio of charges of the two spheres respectively is:}$

Options:

1. $\frac{b}{a}$
2. $\sqrt{ab}$
3. $ab$
4. $\frac{a}{b}$

Solution:

$\text{When two conducting spheres are connected, the potential on both becomes equal.}$ $\text{Let } Q_1 \text{ and } Q_2 \text{ be the charges on spheres of radii } a \text{ and } b \text{ respectively.}$ $\frac{Q_1}{a} = \frac{Q_2}{b}$ $\Rightarrow \frac{Q_1}{Q_2} = \frac{a}{b}$

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
}