Import Question JSON

Current Question (ID: 16494)

Question:

$\text{A ball of mass } 1 \text{ g and charge } 10^{-7} \text{ C moves from a point } A \text{ whose potential is } 500 \text{ V to a point } B \text{ whose potential is zero.}$ $\text{If the speed of the ball at } A \text{ is } 0.51 \text{ m/s, its speed at point } B \text{ will be:}$

Options:

1. $0.6 \text{ m/s}$
2. $6 \text{ m/s}$
3. $2 \text{ m/s}$
4. $4 \text{ m/s}$

Solution:

$\text{Based on conservation of energy (work-energy principle):}$ $\text{Loss in Potential energy = Gain in Kinetic energy}$ $U_i - U_f = \Delta K$ $q(V_A - V_B) = \frac{1}{2} m (v_B^2 - v_A^2)$ $\text{or } 10^{-7} \times (500 - 0) = \frac{1}{2} \times 10^{-3} \times (v_B^2 - 0.51^2)$ $\text{or } v_B^2 = 0.1 + 0.26 = 0.36$ $\therefore v_B = 0.6 \text{ m/s}$

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
}