Import Question JSON

Current Question (ID: 20151)

Question:

$\text{Three concentric shells } A, B \text{ and } C \text{ having surface charge density } \sigma, -\sigma \text{ and } \sigma \text{ respectively.}$ $\text{The radii of } A \text{ and } B \text{ are } 2 \text{ cm and } 3 \text{ cm respectively.}$ $\text{Electric potential at surface } A \text{ is } V_A \text{ and at } C \text{ is } V_C.$ $\text{If } V_A = V_C \text{ then find the radius of } C \text{ in cm}$

Options:

1. $5 \text{ cm}$
2. $7 \text{ cm}$
3. $6 \text{ cm}$
4. $6.5 \text{ cm}$

Solution:

$\text{Hint: } V = \frac{kq}{r}$ $V_A = \frac{K \left( \sigma \times 4\pi a^2 \right)}{a} - \frac{K \left( 4\pi b^2 \right) \sigma}{b} + \frac{K}{c} \left( 4\pi c^2 \right) \sigma$ $V_C = \frac{K}{c} \left( 4\pi a^2 \sigma - 4\pi b^2 \sigma \right) + \frac{K}{c} \left( 4\pi c^2 \right) \sigma$ $V_A = V_C$ $\Rightarrow a - b = \frac{\left( a^2 - b^2 \right)}{c}$ $\Rightarrow a - b = \frac{(a - b)(a + b)}{c}$ $\Rightarrow c = a + b$ $\Rightarrow c = 5 \text{ cm}$

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
}