Import Question JSON

Current Question (ID: 9888)

Question:

$\text{A block of mass } M \text{ is attached to the lower end of a vertical spring. The spring is hung from the ceiling and has a force constant value of } k\text{. The mass is released from rest with the spring initially unstretched. The maximum extension produced along the length of the spring will be:}$

Options:

1. $\frac{Mg}{k}$
2. $\frac{2Mg}{k}$
3. $\frac{4Mg}{k}$
4. $\frac{Mg}{2k}$

Solution:

$\text{Hint: Use the law of conservation of energy.}$ $\text{Step: Find the maximum extension of the spring.}$ $\text{Let } x \text{ be the extension in the spring.}$ $\text{Applying conservation of energy:}$ $mgx = \frac{1}{2}kx^2$ $\Rightarrow x = \frac{2mg}{k}$ $\text{Hence, option (2) is the correct answer.}$

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
}