Import Question JSON

Current Question (ID: 9785)

Question:

$\text{The length of a spring is } l_1 \text{ and } l_2 \text{ when stretched with a force of 4 N and 5 N respectively. Its natural length is?}$

Options:

1. $l_2 + l_1$
2. $2(l_2 - l_1)$
3. $5l_1 - 4l_2$
4. $5l_2 - 4l_1$

Solution:

\text{We use Hooke's law: } F = kx\text{, where } x \text{ is the extension.} \text{For the first case: } 4 = k(l_1 - l_0) \quad \text{...(1)} \text{For the second case: } 5 = k(l_2 - l_0) \quad \text{...(2)} \text{Dividing equation (1) by equation (2): } \frac{4}{5} = \frac{l_1 - l_0}{l_2 - l_0} \text{Solving this equation: } 4(l_2 - l_0) = 5(l_1 - l_0) 4l_2 - 4l_0 = 5l_1 - 5l_0 4l_2 - 5l_1 = 4l_0 - 5l_0 4l_2 - 5l_1 = -l_0 \text{Therefore: } l_0 = 5l_1 - 4l_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
}