Import Question JSON

Current Question (ID: 19899)

Question:

$\text{Two masses } m \text{ and } \frac{m}{2} \text{ are connected at the two ends of a massless rigid rod of length } l. \text{ The rod is suspended by a thin wire of torsional constant } k \text{ at the center of mass of the rod-mass system (see figure).}$ $\text{Because of the torsional constant } k, \text{ the restoring torque is } \tau = k \theta \text{ for angular displacement } \theta. \text{ If the rod is rotated by } \theta_0 \text{ and released, the tension in it when it passes through its mean position will be:}$

Options:

1. $\frac{3k\theta_0^2}{l}$
2. $\frac{2k\theta_0^2}{l}$
3. $\frac{k\theta_0^2}{l}$
4. $\frac{k\theta_0^2}{2l}$

Solution:

$\text{Hint: } T = mr\omega^2$

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
}