Import Question JSON

Current Question (ID: 9715)

Question:

$\text{If two forces } (6\hat{i} + 8\hat{j}) \text{ and } (4\hat{i} + 4\hat{j}) \text{ N are acting on a body of mass 2 kg, then the acceleration produced in the body (in m/s}^2\text{) will be:}$

Options:

1. $(5\hat{i} + 6\hat{j})$
2. $(10\hat{i} + 12\hat{j})$
3. $(6\hat{i} + 12\hat{j})$
4. $(2\hat{i} + 3\hat{j})$

Solution:

$\text{Hint: } \vec{F}_{net} = ma$ $\text{Step 1: Find } \vec{F}_{net}$ $\vec{F}_{net} = 10\hat{i} + 12\hat{j}$ $\text{Step 2: Find acceleration using Newton's second law}$ $\vec{F}_{net} = m\vec{a}$ $\Rightarrow \vec{a} = \frac{10\hat{i} + 12\hat{j}}{2}$ $= 5\hat{i} + 6\hat{j}$

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
}