Import Question JSON

Current Question (ID: 19379)

Question:

$\text{A solid sphere is released from point } O \text{ at the top of an incline as shown.}$ $\text{If the sphere rolls down the inclined plane without slipping,}$ $\text{the velocity of centre of mass of the sphere at the bottommost point}$ $\text{of the incline is: } (g = 10 \text{ m/s}^2)$

Options:

1. $3 \text{ m/s}$
2. $7 \text{ m/s}$
3. $10 \text{ m/s}$
4. $0.7 \text{ m/s}$

Solution:

$\text{Hint: Use energy conservation.}$ $\frac{1}{2}mv_{\text{cm}}^2 + \frac{12}{25}mR^2\left(\frac{v_{\text{cm}}}{R}\right)^2 = mgh$ $\frac{7}{10}mv_{\text{cm}}^2 = mgh$ $v_{\text{cm}} = \sqrt{\frac{10}{7}gh} = 10 \text{ m/s}$

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
}