Import Question JSON

Current Question (ID: 16602)

Question:

$\text{A bullet of mass } 2 \text{ gm has a charge of } 2 \, \mu\text{C. Through what potential difference must it be accelerated, starting from rest, to acquire a speed of } 10 \, \text{m/s?}$

Options:

1. $50 \, \text{kV}$
2. $5 \, \text{V}$
3. $50 \, \text{V}$
4. $5 \, \text{kV}$

Solution:

$\text{The kinetic energy of bullet } K.E = qV$ $\text{ie, } \frac{1}{2} mv^2 = qV$ $\Rightarrow V = \frac{mv^2}{2q}$ $\text{Substituting the values in relation to } V, \text{ we obtain;}$ $V = \frac{2 \times 10^{-3} \times (10)^2}{2 \times 2 \times 10^{-6}}$ $\Rightarrow V = 50 \times 10^3 \, \text{V} = 50\text{kV}$ $\text{Hence, option (1) is the correct answer.}$

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
}