Import Question JSON

Current Question (ID: 8787)

Question:

$\text{A screw gauge gives the following readings when used to measure the diameter of a wire:}$ $\text{Main scale reading: 0 mm}$ $\text{Circular scale reading: 52 divisions}$ $\text{Given that 1 mm on the main scale corresponds to 100 divisions on the circular scale, the diameter of the wire that can be inferred from the given data is:}$

Options:

1. $0.26 \text{ cm}$
2. $0.052 \text{ cm}$
3. $0.52 \text{ cm}$
4. $0.026 \text{ cm}$

Solution:

\text{Hint: The diameter of the wire is given by the sum of the main scale reading and the circular scale reading.} \text{Step 1: Find the least count of the screw gauge.} \text{L.C.} = \frac{\text{Pitch}}{\text{Number of circular scale divisions}} = \frac{1\text{ mm}}{100} = 0.01\text{ mm} \text{Step 2: Find the diameter of the wire.} \text{Diameter of the wire = Reading of the screw gauge = M.S.R + C.S.R} \text{The diameter of the wire is given by,} 0 + 0.01 \times 52 = 0.52\text{ mm} = 0.052\text{ cm} \text{Hence, option (2) 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
}