Import Question JSON

Current Question (ID: 10303)

Question:

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

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 motion, } F_{\text{net}} = 0 \text{ and } \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.}

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
}