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Current Question (ID: 18911)

Question:

$\text{A screw gauge with a pitch of } 0.5 \text{ mm and a circular scale with } 50 \text{ divisions is used to measure the thickness of a thin sheet of Aluminium.}$ $\text{Before starting the measurement, it is found that when the two jaws of the screw gauge are brought in contact, the } 45^{\text{th}} \text{ division coincides with the main scale line and that the zero of the main scale is barely visible.}$ $\text{What is the thickness of the sheet if the main scale reading is } 0.5 \text{ mm and the } 25^{\text{th}} \text{ division coincides with the main scale line?}$

Options:

1. $0.75 \text{ mm}$
2. $0.80 \text{ mm}$
3. $0.70 \text{ mm}$
4. $0.50 \text{ mm}$

Solution:

$\text{Hint: True reading = Observed reading + error.}$ $L.C = \frac{\text{pitch}}{\text{no. of div. on circular scale}} = \frac{0.5 \text{ mm}}{50} = 0.01 \text{ mm}$ $\text{Zero error } e = N \times LC = 5 \times 0.01 = 0.05 \text{ mm}$ $\text{True reading} = \text{observed reading} + e$ $= LSR + CSR \times LC + e$ $= 0.5 \text{ mm} + 25 \times 0.01 + 0.05$ $= 0.75 + 0.05 = 0.80 \text{ mm}$

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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
}