Import Question JSON

Current Question (ID: 19007)

Question:

$\text{In a Vernier caliper, when both jaws touch each other, zero or the Vernier scale shifts towards left and its 4th division coincides exactly with a certain division on main scale. If 50 Vernier scale divisions equal to 49 main scale divisions and zero error in the instrument is 0.04 mm then how many main scale divisions are there in 1 cm?}$

Options:

1. $5$
2. $20$
3. $10$
4. $40$

Solution:

$\text{Given: 50 Vernier scale divisions (VSD) = 49 main scale divisions (MSD)}$ $\text{1 VSD = } \frac{49}{50} \text{ MSD}$ $\text{Least count (LC) = 1 MSD - 1 VSD = 1 MSD - } \frac{49}{50} \text{ MSD}$ $\text{LC = } \frac{1}{50} \text{ MSD}$ $\text{Zero error = 0.04 mm}$ $\text{1 MSD = 0.04 mm}$ $\text{Number of MSD in 1 cm = } \frac{10}{0.04} = 250$

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
}