Import Question JSON

Current Question (ID: 19324)

Question:

$\text{A rectangular solid box of length } 0.3 \text{ m is held horizontally, with one of its sides on the edge of a platform of height } 5 \text{ m.}$ $\text{When released, it slips off the table in a very short time } \tau = 0.01 \text{ s, remaining essentially horizontal.}$ $\text{The angle by which it would rotate when it hits the ground will be (in radians) close to:}$

Options:

1. $0.5$
2. $0.02$
3. $0.28$
4. $0.3$

Solution:

$\text{Hint: } \Delta \theta = \omega t$ $\alpha = \frac{MgL/2}{ML^{2}/3} = \frac{3g}{2L}$ $\omega = \frac{3g}{2L} \tau = \frac{30(0.01)}{2(0.3)} = 0.5$ $t = \sqrt{\frac{2 \times 5}{10}} = 1 \text{ sec}$ $\Delta \theta = \omega t = (0.5)(1) = 0.5 \text{ Rad}$

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
}