Import Question JSON

Current Question (ID: 9652)

Question:

$\text{A stone tied to the end of a 1 m long string is whirled in a horizontal circle at a constant speed. If the stone makes 22 revolutions in 44 seconds, what is the magnitude and direction of acceleration of the stone?}$

Options:

1. $\pi^2 \text{ ms}^{-2} \text{ and direction along the tangent to the circle.}$
2. $\pi^2 \text{ ms}^{-2} \text{ and direction along the radius towards the centre.}$
3. $\frac{\pi^2}{4} \text{ ms}^{-2} \text{ and direction along the radius towards the centre.}$
4. $\pi^2 \text{ ms}^{-2} \text{ and direction along the radius away from the centre.}$

Solution:

\text{Hint: } a_r = \omega^2 r \text{Step: Find the magnitude and direction of acceleration of the stone.} a_r = \omega^2 r = (2\pi n)^2 r = \left(2\pi \times \frac{1}{2}\right)^2 (1) = \pi^2 a_t = 0 \text{Therefore, the magnitude of the acceleration of the stone is } \pi^2 \text{ m/s}^2 \text{and the direction is along the radius towards the centre.} \text{Hence, option (2) 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
}