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Current Question (ID: 19281)

Question:

$\text{A block of mass } m = 0.1 \text{ kg is connected to a spring of unknown spring constant } k. \text{ It is compressed to a distance } x \text{ from rest.}$ $\text{After approaching half the distance } \left( \frac{x}{2} \right) \text{ from the equilibrium position, it hits another identical block and comes to rest momentarily,}$ $\text{while the other block moves with a velocity } 3 \text{ ms}^{-1}. \text{ The total initial energy of the spring is:}$

Options:

1. $0.3 \text{ J}$
2. $0.6 \text{ J}$
3. $1.5 \text{ J}$
4. $0.8 \text{ J}$

Solution:

$\text{Hint: Conservation of mechanical energy.}$

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
}