Import Question JSON

Current Question (ID: 19331)

Question:

$\text{A metal coin of mass } 5 \text{ g and radius } 1 \text{ cm is fixed to a thin stick } AB \text{ of negligible mass as shown in the figure. The system is initially at rest. The constant torque, that will make the system rotate about } AB \text{ at } 25 \text{ rotations per second in } 5 \text{ s, is close to:}$

Options:

1. $7.9 \times 10^{-6} \text{ Nm}$
2. $4.0 \times 10^{-6} \text{ Nm}$
3. $2.0 \times 10^{-5} \text{ Nm}$
4. $1.6 \times 10^{-5} \text{ Nm}$

Solution:

$\text{Hint: } \tau = I \alpha$ $\alpha = \frac{d\omega}{dt} = 10 \pi$ $\tau = I \alpha$ $= \frac{5}{4} \left(MR^2\right) \alpha$ $= 2 \times 10^{-5} \text{ N} \cdot \text{m}$

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
}