Import Question JSON

Current Question (ID: 10259)

Question:

$\text{Four masses are joined to light circular frames as shown in the figure. The radius of gyration of this system about an axis passing through the center of the circular frame and perpendicular to its plane would be:}$ $\text{(where 'a' is the radius of the circle)}$

Options:

1. $\frac{a}{\sqrt{2}}$
2. $\frac{a}{2}$
3. $a$
4. $2a$

Solution:

$\text{Hint: } I = Mk^2$ $\text{Step 1:}$ $\text{Find the moment of inertia of the system}$ $I = 2ma^2 + 3ma^2 + 2ma^2 + ma^2$ $I = 8ma^2$ $\text{Step 2:}$ $\text{Use the concept of the radius of gyration}$ $I = M_{sys}k^2$ $8ma^2 = (8m)k^2$ $\Rightarrow k = a$

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
}