Import Question JSON

Current Question (ID: 19300)

Question:

$\text{A bag of sand of mass } 9.8 \text{ kg is suspended by a rope. A bullet of } 200 \text{ g traveling with speed } 10 \text{ ms}^{-1} \text{ gets embedded in it, then loss of kinetic energy will be:}$

Options:

1. $4.9 \text{ J}$
2. $9.8 \text{ J}$
3. $14.7 \text{ J}$
4. $19.6 \text{ J}$

Solution:

$\text{Initial kinetic energy of the bullet: } \frac{1}{2} \times 0.2 \times (10)^2 = 10 \text{ J}$ $\text{Final kinetic energy of the system: } \frac{1}{2} \times (9.8 + 0.2) \times v^2$ $\text{Using conservation of momentum: } 0.2 \times 10 = (9.8 + 0.2) \times v$ $v = \frac{2}{10} = 0.2 \text{ m/s}$ $\text{Final kinetic energy: } \frac{1}{2} \times 10 \times (0.2)^2 = 0.2 \text{ J}$ $\text{Loss of kinetic energy: } 10 - 0.2 = 9.8 \text{ J}$

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
}