Import Question JSON

Current Question (ID: 10183)

Question:

$\text{A uniform rod of mass m and length l is in uniform translational motion. If one of its ends is suddenly hinged then (hinge is smooth):}$

Options:

1. $\text{It will continue its translational motion.}$
2. $\text{It will now be in pure rotational motion about the hinged end.}$
3. $\text{It will now have combined translational and rotational motion.}$
4. $\text{It will stop.}$

Solution:

\text{Hint: For pure rotational } \vec{F}_{\text{net}} = 0 \text{ and } \vec{\tau}_{\text{net}} \neq 0. \text{Step 1: Identify the motion of the rod.} \text{The rod will start pure rotational motion about the hinge. We can also find the angular velocity of the rod by applying the conservation of angular momentum about the hinge.} \text{When one end of the rod is suddenly hinged, the rod cannot continue its translational motion as the hinged end is now fixed. The rod will undergo pure rotational motion about the hinged end, with the angular velocity determined by conservation of angular momentum.}

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
}