Import Question JSON

Current Question (ID: 16797)

Question:

$\text{Perpendicularly, an electron and a proton enter a magnetic field. Both have the same amount of kinetic energy. Which of the following statements is correct?}$

Options:

1. $\text{Trajectory of electron is less curved}$
2. $\text{Trajectory of proton is less curved}$
3. $\text{Both trajectories are equally curved}$
4. $\text{Both move on a straight-line path}$

Solution:

$\text{(b) We have } qvB = \frac{mv^2}{r} \text{ or } r = \frac{mv}{qB} = \frac{\sqrt{2mK}}{qB}$ $\text{For same kinetic energy } K, \text{ we have } r \propto \frac{\sqrt{m}}{q}$ $\text{Hence path of proton will have larger } r \text{ and is therefore less curved.}$

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
}