Import Question JSON

Current Question (ID: 9837)

Question:

$\text{The relationship between force and position is shown in the given figure (in a one-dimensional case). The work done by the force in displacing a body from } x = 1 \text{ cm to } x = 5 \text{ cm is:}$

Options:

1. $20 \text{ ergs}$
2. $60 \text{ ergs}$
3. $70 \text{ ergs}$
4. $700 \text{ ergs}$

Solution:

$\text{Work done = area between the graph and position axis}$ $\text{From the graph, we can calculate the area under the curve from } x = 1 \text{ cm to } x = 5 \text{ cm:}$ $\text{From } x = 1 \text{ to } x = 2: F = 10 \text{ dyne, area} = 10 \times 1 = 10 \text{ erg}$ $\text{From } x = 2 \text{ to } x = 3: F = 20 \text{ dyne, area} = 20 \times 1 = 20 \text{ erg}$ $\text{From } x = 3 \text{ to } x = 4: F = -20 \text{ dyne, area} = -20 \times 1 = -20 \text{ erg}$ $\text{From } x = 4 \text{ to } x = 5: F = 10 \text{ dyne, area} = 10 \times 1 = 10 \text{ erg}$ $W = 10 + 20 + (-20) + 10 = 20 \text{ erg}$ $\text{Therefore, option (1) is the correct answer.}$

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
}