Import Question JSON

Current Question (ID: 19297)

Question:

$\text{A stone tied to a string of length } L \text{ is whirled in a vertical circle with the other end of the string at the centre.}$ $\text{At a certain instant of time, the stone is at its lowest position and has a speed } u. \text{The magnitude of change in its velocity, as it reaches a position where the string is horizontal, is } \sqrt{x \left( u^2 - gL \right)}. \text{The value of } x \text{ is:}$

Options:

1. $3$
2. $2$
3. $1$
4. $5$

Solution:

$\text{The change in velocity when the stone moves from the lowest point to the horizontal position is given by the equation:}$ $\Delta v = \sqrt{u^2 - gL} - 0 = \sqrt{u^2 - gL}.$ $\text{The expression given is } \sqrt{x \left( u^2 - gL \right)}. \text{Comparing both expressions, we find } x = 2.$

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
}