Import Question JSON

Current Question (ID: 9711)

Question:

$\text{A particle moves from a point } (-2\hat{i} + 5\hat{j}) \text{ to } (4\hat{j} + 3\hat{k}) \text{ when a force of } (4\hat{i} + 3\hat{j}) \text{ N is applied. How much work has been done by the force?}$

Options:

1. $8 \text{ J}$
2. $11 \text{ J}$
3. $5 \text{ J}$
4. $2 \text{ J}$

Solution:

$\text{Hint: } W = \vec{F} \cdot d\vec{s}$ $\text{Step 1: Find the displacement of the particle.}$ $\Delta \vec{s} = \vec{r}_2 - \vec{r}_1$ $= 4\hat{j} + 3\hat{k} - (-2\hat{i} + 5\hat{j})$ $= 2\hat{i} - \hat{j} + 3\hat{k}$ $\text{Step 2: Find the force on the particle.}$ $\vec{F} = 4\hat{i} + 3\hat{j} \text{ N}$ $\therefore \text{ Work done, } W = \vec{F} \cdot \Delta \vec{s}$ $= (4\hat{i} + 3\hat{j}) \cdot (2\hat{i} - \hat{j} + 3\hat{k})$ $= 8 - 3 = 5\text{J}$

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
}