Import Question JSON

Current Question (ID: 19146)

Question:

$\text{A boy pushes a box of mass } 2 \text{ kg with a force } \vec{F} = (20\hat{i} + 10\hat{j}) \text{ N}$ $\text{on a frictionless surface. If the box was initially at rest, then the displacement along the } x\text{-axis after } 10 \text{ s is:}$

Options:

1. $100 \text{ m}$
2. $300 \text{ m}$
3. $500 \text{ m}$
4. $700 \text{ m}$

Solution:

$\text{Hint: } \vec{s} = \vec{u}t + \frac{1}{2} \vec{a} t^2$ $\vec{F} = (20\hat{i} + 10\hat{j}) \text{ N}$ $\vec{a} = \frac{\vec{F}}{m} = \frac{20\hat{i} + 10\hat{j}}{2} \Rightarrow 10\hat{i} + 5\hat{j}$ $\therefore \vec{s} = \frac{1}{2} \vec{a} t^2 = \frac{1}{2} (10\hat{i} + 5\hat{j}) \times (10)^2$ $\Rightarrow 50 (10\hat{i} + 5\hat{j}) \text{ m}$ $\therefore \text{Displacement along } x\text{-axis}$ $\Rightarrow 50 \times 10 = 500 \text{ m}$ $\therefore \text{Ans. } 500$

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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
}