Import Question JSON

Current Question (ID: 9866)

Question:

$\text{A spring 40 mm long is stretched by the application of force. If 10 N force is required to stretch the spring through 1 mm, then work done to stretch the spring 40 mm is equal to:}$

Options:

1. $84 \text{ J}$
2. $68 \text{ J}$
3. $23 \text{ J}$
4. $8 \text{ J}$

Solution:

$\text{Given: Force required to stretch spring through 1 mm = 10 N}$ $\text{First, we find the spring constant:}$ $k = \frac{F}{x} = \frac{10}{1 \times 10^{-3}} = 10^4 \text{ N/m}$ $\text{Work done to stretch the spring by 40 mm (40 × 10⁻³ m):}$ $W = \frac{1}{2}kx^2 = \frac{1}{2} \times 10^4 \times (40 \times 10^{-3})^2 = 8 \text{ J}$

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
}