Import Question JSON

Current Question (ID: 9722)

Question:

$\text{An object of mass 3 kg is at rest. Now if a force of } \vec{F} = 6t^2\hat{i} + 4t\hat{j} \text{ is applied to the object, then the velocity of the object at } t = 3 \text{ second will be:}$

Options:

1. $18\hat{i} + 3\hat{j}$
2. $18\hat{i} + 6\hat{j}$
3. $3\hat{i} + 18\hat{j}$
4. $18\hat{i} + 4\hat{j}$

Solution:

\vec{a} = \frac{\vec{F}}{m} = 2t^2\hat{i} + \frac{4}{3}t\hat{j} d\vec{v} = \left(2t^2\hat{i} + \frac{4}{3}t\hat{j}\right) dt \text{Integrate on both sides} \vec{v} = 2 \cdot \frac{t^3}{3}\hat{i} + \frac{4}{3} \cdot \frac{t^2}{2}\hat{j} \text{At } t = 3 \text{ sec, } \vec{v} = \frac{2}{3} \times (3)^3\hat{i} + \frac{4}{6} \times (3)^2\hat{j} = 18\hat{i} + 6\hat{j}

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
}