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Current Question (ID: 20480)

Question:

$\text{A dipole having moment } M \text{ is placed in two magnetic fields of strength } B_1 \text{ and } B_2 \text{ respectively.}$ $\text{If the dipole oscillates 60 times in 20 s in } B_1 \text{ and 60 oscillations in 30 s in } B_2 . \text{ Then } \frac{B_1}{B_2} =$

Options:

1. $\frac{3}{2}$
2. $\frac{2}{3}$
3. $\frac{4}{9}$
4. $\frac{9}{4}$

Solution:

$\text{Hint: } \tau = \vec{M} \times \vec{B}$ $\tau = \vec{M} \times \vec{B}$ $I \alpha = -MB \theta$ $\alpha = -\left( \frac{MB}{I} \right) \theta \Rightarrow \frac{20}{30} = \sqrt{\frac{B_2}{B_1}}$ $T = 2\pi \sqrt{\frac{I}{MB}} \Rightarrow \frac{B_1}{B_2} = \frac{9}{4}$ $\frac{T_1}{T_2} = \sqrt{\frac{B_2}{B_1}}$

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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
}