Import Question JSON

Current Question (ID: 8790)

Question:

$\text{Consider a screw gauge without any zero error. What will be the final reading corresponding to the final state as shown?}$ $\text{It is given that the circular head translates } P \text{ MSD in } N \text{ rotations. (1 MSD} = 1 \text{ mm.)}$ $\text{The circular scale has 100 divisions}$

Options:

1. $\left(\frac{P}{N}\right)\left(2 + \frac{45}{100}\right) \text{ mm}$
2. $\left(\frac{N}{P}\right)\left(2 + \frac{45}{N}\right) \text{ mm}$
3. $P\left(\frac{2}{N} + \frac{45}{100}\right) \text{ mm}$
4. $\left(2 + \frac{45}{100} \times \frac{P}{N}\right) \text{ mm}$

Solution:

\text{Hint: L.C.} = \frac{\text{Pitch}}{\text{Number of circular scale divisions}} \text{Step: Find the final reading of the screw gauge.} \text{Pitch} = \frac{P}{N} \text{ mm} \text{L.C.} = \frac{P}{100N} \text{ mm} \text{Reading of the screw gauge} = 2 \text{ mm} + \left(\frac{P}{100N} \times 45\right) \text{ mm} \text{Therefore, the final reading of the screw gauge is} \left(2 + \frac{45P}{100N}\right) \text{ mm} \text{Hence, option (4) 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
}