Import Question JSON

Current Question (ID: 9641)

Question:

$\text{A body is projected with a velocity } u \text{ with an angle of projection } \theta\text{. Change in velocity after the time } (t) \text{ from the time of projection will be:}$

Options:

1. $gt$
2. $\frac{1}{2}gt^2$
3. $u \sin \theta$
4. $u \cos \theta$

Solution:

\text{Hint: } \vec{u} = u \cos \theta \hat{i} + u \sin \theta \hat{j} \text{Step: Find the change in velocity after time t from projection.} \text{Initial velocity: } \vec{u} = u \cos \theta \hat{i} + u \sin \theta \hat{j} \text{Velocity after time t: } \vec{v} = u \cos \theta \hat{i} + (u \sin \theta - gt) \hat{j} \text{Change in velocity: } \Delta \vec{v} = \vec{v} - \vec{u} \Delta \vec{v} = u \cos \theta \hat{i} + (u \sin \theta - gt) \hat{j} - (u \cos \theta \hat{i} + u \sin \theta \hat{j}) \Delta \vec{v} = -gt \hat{j} \text{Magnitude: } |\Delta \vec{v}| = gt \text{Therefore, option (1) is correct.}

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
}