Import Question JSON

Current Question (ID: 18966)

Question:

$\text{If surface tension } (S), \text{ Moment of Inertia } (I) \text{ and Planck's constant } (h), \text{ were to be taken as the fundamental units, the dimensional formula for linear momentum would be:}$

Options:

1. $S^{3/2}I^{1/2}h^0$
2. $S^{1/2}I^{1/2}h^{-1}$
3. $S^{1/2}I^{3/2}h^{-1}$
4. $S^{1/2}I^{1/2}h^0$

Solution:

$\text{Hint: } P \propto \sqrt{\text{mass} \times \text{Energy}}$ $p \propto \sqrt{\text{mass} \times \text{Energy}}$ $\propto \sqrt{mR^2S}$ $\propto \sqrt{IS}$ $[p] = [I^{1/2}S^{1/2}]$

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
}