Import Question JSON

Current Question (ID: 19222)

Question:

$\text{A large number } (n) \text{ of identical beads, each of mass } m \text{ and radius } r$ $\text{are strung on a thin smooth rigid horizontal rod of length } L (L \gg r)$ $\text{and are at rest at random positions. The rod is mounted}$ $\text{between two rigid supports (see figure). If one of the beads is now}$ $\text{given a speed } v, \text{ the average force experienced by each support after}$ $\text{a long time is: (assume all collisions are elastic)}$

Options:

1. $\frac{mv^2}{2(L-nr)}$
2. $\frac{mv^2}{L-2nr}$
3. $\frac{mv^2}{L-nr}$
4. $\text{zero}$

Solution:

$\text{Hint: } F = \frac{\Delta P}{\Delta t}$

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
}