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Current Question (ID: 19012)

Question:

$\text{The diameter of a sphere is measured using a vernier caliper whose }$ $9 \text{ divisions of main scale are equal to } 10 \text{ divisions of vernier scale.}$ $\text{The shortest division on the main scale is equal to } 1 \text{ mm.}$ $\text{The main scale reading is } 2 \text{ cm and second division of vernier scale}$ $\text{coincides with a division on main scale.}$ $\text{If mass of the sphere is } 8.635 \text{ g, the density of the sphere is:}$

Options:

1. $2.5 \text{ g/cm}^3$
2. $1.7 \text{ g/cm}^3$
3. $2.0 \text{ g/cm}^3$
4. $2.2 \text{ g/cm}^3$

Solution:

$\text{The vernier constant (V.C.) is given by:}$ $\text{V.C.} = 1 \text{ mm} \times \frac{1}{10} = 0.1 \text{ mm}$ $\text{Total reading} = \text{Main scale reading} + (\text{Vernier scale reading} \times \text{V.C.})$ $= 2 \text{ cm} + (2 \times 0.1 \text{ mm}) = 2.02 \text{ cm}$ $\text{Diameter of sphere} = 2.02 \text{ cm}$ $\text{Radius of sphere} = \frac{2.02}{2} = 1.01 \text{ cm}$ $\text{Volume of sphere} = \frac{4}{3} \pi (1.01)^3 \text{ cm}^3$ $= 4.32 \text{ cm}^3$ $\text{Density} = \frac{\text{Mass}}{\text{Volume}} = \frac{8.635}{4.32} \text{ g/cm}^3$ $= 2.0 \text{ g/cm}^3$

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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
}