Import Question JSON

Current Question (ID: 9855)

Question:

$\text{A bullet fired towards a wall reduces its kinetic energy by half after the penetration of 6 cm. The further penetration of the bullet into the wall is:}$

Options:

1. $2 \text{ cm}$
2. $1 \text{ cm}$
3. $6 \text{ cm}$
4. $3 \text{ cm}$

Solution:

$\text{Hint: Apply work-energy theorem.}$ $\text{Step 1: Apply work-energy theorem for first 6 cm penetration.}$ $W_R = \Delta K$ $-Fx = \frac{K}{2} - K$ $-6F = \frac{K}{2} \ldots\ldots\ldots(1)$ $\text{Step 2: Apply work-energy theorem from 6cm penetration to final point.}$ $-Fx_1 = 0 - \frac{K}{2} \ldots\ldots\ldots(2)$ $-Fx_1 = -6F$ $x_1 = 6 \text{ cm}$

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
}