Import Question JSON

Current Question (ID: 9574)

Question:

$\text{A particle is moving with velocity } \vec{v} = k(y\hat{i} + x\hat{j}) \text{ where } k \text{ is a constant. The general equation for the path will be:}$

Options:

1. $y = x^2 + \text{constant}$
2. $y^2 = x^2 + \text{constant}$
3. $y = x + \text{constant}$
4. $xy = \text{constant}$

Solution:

$\text{Hint: } v_x = \frac{dx}{dt}$ $\text{Step: Find the general equation of the path of the particle.}$ $\vec{v} = k(y\hat{i} + x\hat{j})$ $\vec{v} = v_x \hat{i} + v_y \hat{j}$ $v_x = \frac{dx}{dt} = ky$ $\frac{dx}{dy}(kx) = ky$ $\int kx dx = \int ky dy$ $y^2 = x^2 + \text{constant}$ $\text{Hence, option (2) is the correct answer.}$

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
}