Import Question JSON

Current Question (ID: 16902)

Question:

$\text{A vibration magnetometer consists of two identical bar magnets placed one over the other such that they are perpendicular and bisect each other. The time period of oscillation in a horizontal magnetic field is } 2 \frac{5}{4} \text{ seconds. One of the magnets is removed and if the other magnet oscillates in the same field, then the time period in seconds is:}$

Options:

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

Solution:

$\text{Initially magnetic moment of system } M_1 = \sqrt{M^2 + M^2} = \sqrt{2}M$ $\text{and the moment of inertia } I_1 = I + I = 2I$ $\text{Finally when one of the magnets is removed, then:}$ $M_2 = M \text{ and } I_2 = I$ $\text{So } T = 2\pi \sqrt{\frac{I}{MB_H}}$ $\frac{T_1}{T_2} = \sqrt{\frac{I_1}{I_2} \times \frac{M_2}{M_1}} = \sqrt{\frac{2I}{I} \times \frac{M}{\sqrt{2}M}} \Rightarrow T_2 = \frac{2^{5/4}}{2^{1/4}} = 2 \text{ sec.}$

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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
}