Import Question JSON

Current Question (ID: 9870)

Question:

$\text{Two springs of spring constants } k \text{ and } 3k \text{ are stretched separately by the same force. The ratio of potential energy stored in them respectively, will be:}$

Options:

1. $3 : 1$
2. $9 : 1$
3. $1 : 3$
4. $1 : 9$

Solution:

\text{The potential energy stored in the spring: } U = \frac{1}{2}kx^2 = \frac{(kx)^2}{2k} = \frac{F^2}{2k} \text{Therefore: } U \propto \frac{1}{k} \text{So: } \frac{U_1}{U_2} = \frac{k_2}{k_1} = \frac{3k}{k} = 3

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
}