Import Question JSON

Current Question (ID: 10217)

Question:

$\text{If the radius of the earth is suddenly contracted to half of its present value, then the duration of the day will be of:}$

Options:

1. $\text{6 hours}$
2. $\text{12 hours}$
3. $\text{18 hours}$
4. $\text{24 hours}$

Solution:

$\text{Angular momentum of earth is constant.}$ $I\omega = \text{constant}$ $\frac{2}{5}MR^2 \times \frac{2\pi}{T} = \text{Constant}$ $T \propto R^2, \text{ if radius becomes half then time period of rotation becomes 1/4 of the previous value.}$ $T_{new} = 24/4 = 6 \text{ hrs.}$

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
}