Import Question JSON

Current Question (ID: 10348)

Question:

$\text{Anvils made of single crystals of diamond, with the shape as shown in the figure, are used to investigate the behaviour of materials under very high pressures. Flat faces at the narrow end of the anvil have a diameter of 0.50 mm, and the wide end are subjected to a compressional force of 50,000 N. What is the pressure at the tip of the anvil?}$

Options:

1. $2.5 \times 10^{11} \text{ Pa}$
2. $3.7 \times 10^{11} \text{ Pa}$
3. $2.1 \times 10^{11} \text{ Pa}$
4. $1.9 \times 10^{11} \text{ Pa}$

Solution:

$\text{Hint: Force at the narrow end will be the same as it is applied at the flat faces.}$ $\text{Step 1: Calculate the pressure from given values.}$ $\text{The diameter of the cones at the edges, } d = 0.5 \times 10^{-3} \text{ m}$ $\text{Radius } = \frac{d}{2} = 0.25 \times 10^{-3} \text{ m}$ $\text{Compression force, } F = 50000 \text{ N}$ $\text{Pressure at the tip of the anvil,}$ $P = \frac{\text{Force}}{\text{Area}} = \frac{50000}{\pi \times (0.25 \times 10^{-3})^2} = 2.55 \times 10^{11} \text{ Pa}$

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
}