Import Question JSON

Current Question (ID: 9658)

Question:

$\text{A stone tied to the end of a string 80 cm long is whirled in a horizontal circle at a constant speed. If the stone makes 14 revolutions in 25 s, what is the magnitude of the acceleration of the stone?}$

Options:

1. $8.1 \text{ ms}^{-2}$
2. $7.7 \text{ ms}^{-2}$
3. $8.7 \text{ ms}^{-2}$
4. $9.9 \text{ ms}^{-2}$

Solution:

\text{Hint: The time required to complete one revolution is the time period of the revolution.} \text{Step 1: Here, the stone completes 14 revolutions in 25 sec. Hence, time to complete one revolution = } \frac{25}{14} \text{ sec.} \text{Step 2: Find the acceleration of the stone.} \omega = \frac{2\pi}{T} \text{And,} a_R = \omega^2 R a_R = 0.8 \times \left(\frac{14 \times 2\pi}{25}\right)^2 a_R \approx 9.9 \text{ m/s}^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
}