Import Question JSON

Current Question (ID: 19417)

Question:

$\text{A person with a mass of } 80 \text{ kg is standing on the rim of a circular platform with a mass of } 200 \text{ kg and rotating about its axis at a speed of } 5 \text{ revolutions per minute (rpm). As the person moves toward the centre of the platform, what will be the platform's new rotational speed (in rpm) once the person reaches its centre?}$ $1.\ 3$ $2.\ 6$ $3.\ 9$ $4.\ 12$

Options:

1. $3$
2. $6$
3. $9$
4. $12$

Solution:

$\text{Hint: Apply the conservation of angular momentum.}$ $\text{Step: Find the rotational speed of the platform.}$ $\text{According to the conservation of angular momentum;} \ L_i = L_f$ $\Rightarrow \left(80R^2 + \frac{200R^2}{2}\right) \omega_i = \left(0 + \frac{200R^2}{2}\right) \omega_f$ $\Rightarrow 180\omega_i = 100\omega_f$ $\Rightarrow \omega_f = 1.8\omega_i = 1.8 \times 5$ $\Rightarrow \omega_f = 9 \text{ rpm}$ $\text{Hence, option (3) is the correct answer.}$

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
}