Import Question JSON

Current Question (ID: 10325)

Question:

$\text{If a particle moves in a circle with a constant angular speed } (\omega) \text{ about the point } O\text{, then its angular speed about the point } A \text{ will be:}$

Options:

1. $\frac{2\omega}{\omega}$
2. $\frac{\omega}{2}$
3. $\omega$
4. $\frac{\omega}{4}$

Solution:

\text{The linear speed of the particle is } v = \omega R. \text{Consider the particle at point B. The distance from A to B is the diameter, } 2R\text{. The linear velocity } v \text{ is perpendicular to the line AB.} \text{The angular speed about A at this instant is } \omega_A = \frac{\text{linear speed}}{\text{distance from A}} = \frac{v}{2R}. \text{Substitute } v = \omega R\text{:} \omega_A = \frac{\omega R}{2R} = \frac{\omega}{2} \text{This angular speed about A is constant throughout the motion.}

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
}