Import Question JSON

Current Question (ID: 9593)

Question:

$\text{A particle has an initial velocity } (2\hat{i} + 3\hat{j}) \text{ and an acceleration } (0.3\hat{i} + 0.2\hat{j}). \text{ The magnitude of velocity after 10 s will be:}$

Options:

1. $9\sqrt{2} \text{ units}$
2. $5\sqrt{2} \text{ units}$
3. $5 \text{ units}$
4. $9 \text{ units}$

Solution:

$\text{Hint: Use 1st equation of motion.}$ $\text{Step: Use the vector form of 1st equation.}$ $\vec{v} = \vec{u} + \vec{a}t$ $= (2\hat{i} + 3\hat{j}) + (0.3\hat{i} + 0.2\hat{j}) \times 10$ $= (2\hat{i} + 3\hat{j}) + (3\hat{i} + 2\hat{j})$ $= 5\hat{i} + 5\hat{j}$ $\text{The magnitude of velocity is:}$ $v = \sqrt{v_x^2 + v_y^2}$ $= \sqrt{5^2 + 5^2}$ $= \sqrt{25 + 25}$ $= \sqrt{50}$ $= 5\sqrt{2} \text{ units}$ $\text{Hence, option (2) is the correct answer.}$

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
}