Import Question JSON

Current Question (ID: 19215)

Question:

$\text{A car of } 800 \text{ kg is taking turn on a banked road of radius } 300 \text{ m and angle of banking } 30^\circ . \text{ If coefficient of static friction is } 0.2 \text{ then the maximum speed with which car can negotiate the turn safely : } ( g = 10 \text{ m/s}^2 , \sqrt{3} = 1.73 )$

Options:

1. $51.4 \text{ m/s}$
2. $102.8 \text{ m/s}$
3. $70.4 \text{ m/s}$
4. $264 \text{ m/s}$

Solution:

$\text{The maximum speed } v \text{ is given by the formula:}$ $v = \sqrt{r g (\tan \theta + \mu_s)}$ $\text{where } r = 300 \text{ m, } g = 10 \text{ m/s}^2, \theta = 30^\circ, \mu_s = 0.2$ $v = \sqrt{300 \times 10 \times (\tan 30^\circ + 0.2)}$ $\tan 30^\circ = \frac{1}{\sqrt{3}} = 0.577$ $v = \sqrt{3000 \times (0.577 + 0.2)}$ $v = \sqrt{3000 \times 0.777}$ $v = \sqrt{2331}$ $v \approx 51.4 \text{ m/s}$

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
}