Import Question JSON

Current Question (ID: 10181)

Question:

$\text{A particle is moving with a constant velocity along a line parallel to the positive x-axis. The magnitude of its angular momentum with respect to the origin is:}$

Options:

1. $\text{zero}$
2. $\text{increasing with } x$
3. $\text{decreasing with } x$
4. $\text{remaining constant}$

Solution:

\text{Hint: Angular momentum is constant if the perpendicular distance is constant.} \text{Step 1: Draw the diagram} \text{The diagram shows a coordinate system with the particle moving along a line parallel to the positive x-axis with velocity } \vec{v}\text{.} \text{Step 2: Analysis} \text{Angular momentum is given as } \vec{L} = \vec{r} \times \vec{p} \text{The magnitude is } L = pr\sin\theta \text{From the given figure above, the perpendicular distance of the particle from the x-axis remains constant.} \text{Therefore, the magnitude of its angular momentum with respect to the origin remains constant.}

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
}