Import Question JSON

Current Question (ID: 19406)

Question:

$\text{A uniform thin rod } AB \text{ of length } L \text{ has linear mass density } \mu(x) = a + \frac{bx}{L}, \text{ where } x \text{ is measured from } A.$ $\text{If the centre of mass of the rod lies at a distance of } \left(\frac{7}{12}\right)L \text{ from } A, \text{ then } a \text{ and } b \text{ are related as:}$

Options:

1. $a = 2b$
2. $2a = b$
3. $a = b$
4. $3a = 2b$

Solution:

$\text{Hint: } X_{\text{COM}} = \frac{\int x \, dm}{\int dm}$

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
}