Import Question JSON

Current Question (ID: 16798)

Question:

$\text{A charged particle is projected in a uniform magnetic field at an angle of } 45^\circ \text{ to the magnetic field.}$ $\text{If the circumference of the helical path followed by it is } 2 \text{ cm, then the pitch of the helix will be:}$

Options:

1. $1 \text{ cm}$
2. $\sqrt{2} \text{ cm}$
3. $2 \text{ cm}$
4. $4 \text{ cm}$

Solution:

$\text{The pitch of the helix is given by } p = \frac{2\pi v_{\parallel}}{\omega}.$ $\text{Here, } v_{\parallel} = v \cos 45^\circ \text{ and } \omega = \frac{qB}{m}.$ $\text{Given circumference } = 2 \text{ cm, which implies } 2\pi r = 2 \text{ cm, so } r = \frac{1}{\pi} \text{ cm}.$ $\text{Thus, } p = \frac{2\pi \cdot v \cdot \cos 45^\circ}{\frac{qB}{m}} = 2 \text{ cm}.$

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
}