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Current Question (ID: 8792)

Question:

$\text{A screw gauge has some zero error but its value is unknown. We have two identical rods. When the first rod is inserted in the screw, the state of the instrument is shown by diagram (I). When both the rods are inserted together in series then the state is shown by the diagram (II). What is the zero error of the instrument?}$ $1 \text{ msd} = 100 \text{ csd} = 1 \text{ mm}$

Options:

1. $-0.16 \text{ mm}$
2. $+0.16 \text{ mm}$
3. $+0.14 \text{ mm}$
4. $-0.14 \text{ mm}$

Solution:

\text{Hint: Correct reading = Observed reading - Zero error.} \text{Step: Find the zero error of the instrument.} \text{Let the thickness of the rod be } t \text{ and let the zero error of the instrument be } x. \text{ It will remain the same in each reading.} \text{L.C.} = \frac{1}{100} \text{ mm} = 0.01 \text{ mm} \text{Correct reading = Observed reading - Zero error} \text{Case 1: Using equation 1} t = (2 + 0.01 \times 12) \text{ mm} - x \text{Case 2: Using equation 1,} 2t = (4 + 0.01 \times 10) \text{ mm} - x \text{(Equation 3) - 2 (Equation 2)} \text{we get } x = 0.14 \text{ mm} \text{Hence, option (3) is the correct answer.}

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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
}