Import Question JSON

Current Question (ID: 19660)

Question:

$\text{A uniform rectangular plate has a circular hole of diameter } d \text{ as shown in the figure. The coefficient of linear expansion of the plate is } \alpha. \text{ What will be the change in the diameter of the hole if the temperature of the plate is increased by } \Delta T?$

Options:

1. $2\alpha \Delta T$
2. $d \alpha \Delta T$
3. $\frac{d}{2} \alpha \Delta T$
4. $3\alpha \Delta T$

Solution:

$\text{Hint: } \frac{\Delta L}{L} = \alpha \Delta T$ $\text{Step: Find the change in the diameter of the hole.}$ $\frac{\Delta d}{d} = \alpha \Delta T$ $\Rightarrow \Delta d = d \alpha \Delta T$ $\text{Hence, option (2) is the correct option.}$

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
}