Import Question JSON

Current Question (ID: 10294)

Question:

$\text{Two discs are rotating about their axes, normal to the discs and passing through the centres of the discs. Disc } D_1 \text{ has a 2 kg mass, 0.2 m radius, and an initial angular velocity of 50 rad s}^{-1}\text{. Disc } D_2 \text{ has 4 kg mass, 0.1 m radius, and initial angular velocity of 200 rad s}^{-1}\text{. The two discs are brought in contact face to face, with their axes of rotation coincident. The final angular velocity (in rad.s}^{-1}\text{) of the system will be:}$

Options:

1. $60$
2. $100$
3. $120$
4. $40$

Solution:

$\text{By conserving the angular momentum,}$ $(I_1 + I_2)\omega_f = I_1\omega_1 + I_2\omega_2$ $\omega_f = \frac{I_1\omega_1 + I_2\omega_2}{I_1 + I_2} = \frac{\frac{1}{2}m_1R_1^2\omega_1 + \frac{1}{2}m_2R_2^2\omega_2}{\frac{1}{2}m_1R_1^2 + \frac{1}{2}m_2R_2^2} = 100 \text{ rad s}^{-1}$

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
}