Import Question JSON

Current Question (ID: 9791)

Question:

$\text{A small coin is kept at a distance } r \text{ from the centre of a gramophone disc rotating at an angular speed } \omega\text{. The minimum coefficient of friction for which a coin will not slip is:}$

Options:

1. $\frac{r\omega^2}{g}$
2. $\frac{g}{r\omega^2}$
3. $\frac{r^2\omega^2}{g}$
4. $\frac{r\omega}{g}$

Solution:

$\text{Hint: Centripetal force on the coin is provided by the frictional force.}$ $\text{Step 1: Here, } f = m\omega^2 r$ $\text{Step 2: As the coin does not slip on the disc:}$ $f \geq m\omega^2 r$ $\mu mg \geq m\omega^2 r$ $\mu \geq \frac{\omega^2 r}{g}$

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
}