Import Question JSON

Current Question (ID: 19909)

Question:

$\text{Point A moves with a uniform speed along the circumference of a circle of radius } 0.36 \text{ m and covers } 30^\circ \text{ in } 0.1 \text{ s.}$ $\text{The perpendicular projection 'P' from 'A' on the diameter MN represents the simple harmonic motion of 'P'.}$ $\text{The restoration force per unit mass when P touches M will be:}$

Options:

1. $100 \text{ N}$
2. $0.49 \text{ N}$
3. $50 \text{ N}$
4. $9.87 \text{ N}$

Solution:

$\text{Hint: } F = -kx = m\omega^2 A$ $30^\circ \rightarrow 0.1 \text{ s}$ $360^\circ \rightarrow 1.2 \text{ s} = T$ $\omega = \frac{2\pi}{T} = \frac{5\pi}{3}$ $\text{At M, } F = m\omega^2 A \Rightarrow \frac{F}{m} = \omega^2 A$

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
}