Import Question JSON

Current Question (ID: 10361)

Question:

Two wires $X$ and $Y$ of the same length are made of the same material. The figure represents the load $F$ versus extension $\Delta x$ graph for the two wires. Hence:

Options:

1. Modulus of elasticity of $Y$ is greater than that of $X$.
2. Stiffness of $Y$ is more than that of $X$.
3. The cross-sectional area of $Y$ is less than that of $X$.
4. All of these

Solution:

Stiffness is the measurement of the resistance of the material against the deformation when a force is applied on it. The slope of the $F-\Delta x$ graph gives stiffness. As the slope of $Y$ is greater than the slope of $X$. Thus, the stiffness of $Y$ is more than that of $X$.

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
}