Import Question JSON

Current Question (ID: 16772)

Question:

$\text{A particle of mass } m, \text{ charge } Q, \text{ and kinetic energy } T \text{ enters a transverse uniform magnetic field of induction } \vec{B}. \text{ What will be the kinetic energy of the particle after seconds?}$

Options:

1. $3T$
2. $2T$
3. $T$
4. $4T$

Solution:

$\text{Hint: The work done by the magnetic force is zero.}$ $\text{Explanation: When a charged particle having a given (K.E.) (T) enters in a field of magnetic induction, which is perpendicular to its velocity, it takes a circular trajectory. It does not increase in energy, therefore (T) is the (K.E.).}$ $\text{After passing through a magnetic field, the magnitude of its mass and velocity of the particle remains the same, so its energy does not change, i.e., kinetic energy will remain (T).}$ $\text{Hence, option (3) is the correct answer.}$

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
}