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Current Question (ID: 18914)

Question:

$\text{In the formula } X = 5YZ^2, X \text{ and } Z \text{ have dimensions of}$ $\text{capacitance and magnetic field, respectively. What are the}$ $\text{dimensions of } Y \text{ in SI units?}$

Options:

1. $[M^{-3}L^{-2}T^8A^4]$
2. $[M^{-2}L^{-2}T^6A^3]$
3. $[M^{-1}L^{-2}T^4A^2]$
4. $[M^{-2}L^0T^{-4}A^{-2}]$

Solution:

$\text{Hint: Recall the dimensions of } X \text{ and } Z.$ $X = 5YZ^2$ $X = \text{Capacitance} = \frac{Q}{V}$ $= \frac{Q^2}{\omega} = \frac{Q^2}{A^2T^2} \cdot \frac{F \cdot L}{M^1L^1T^{-2} \cdot L}$ $= A^2M^{-1}L^{-2}T^4$ $Z^2 = M^2T^{-4}A^{-2}$ $Y = \frac{X}{Z^2} = \frac{M^{-1}L^{-2}T^4A^2}{M^2T^{-4}A^{-2}}$ $= M^{-3}L^{-2}T^8A^4$

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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
}