Import Question JSON

Current Question (ID: 19053)

Question:

$\text{A bullet is fired into a fixed target. It loses } \frac{1}{3} \text{ rd of its velocity after travelling } 4 \text{ cm. It penetrates further } p \times 10^{-3} \text{ m before coming to rest. Find } p.$

Options:

1. 35
2. 30
3. 40
4. 32

Solution:

$v^2 - u^2 = 2as$ $\text{Let } v_0 : \text{initial}$ $\Rightarrow \left(\frac{2v_0}{3}\right)^2 - v_0^2 = 2(-a)\left(\frac{4}{100}\right) \quad \text{(i)}$ $\Rightarrow \frac{5}{9}v_0^2 = \frac{2a}{25}$ $\text{Also, } \frac{4v_0^2}{9} = 2 \times a \times (p \times 10^{-3}) \quad \text{(ii)}$ $\Rightarrow \frac{5}{4} = \frac{1000}{25 \times p}$ $\Rightarrow p = 32$

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
}