Import Question JSON

Current Question (ID: 10746)

Question:

$\text{If the same amount of heat is supplied to two spheres of the same material having the same radius (one is hollow and the other is solid), then:}$

Options:

1. $\text{the expansion in hollow is greater than the expansion in solid}$ (Correct)
2. $\text{the expansion in hollow is the same as that in solid}$
3. $\text{the expansion in hollow is lesser than in solid}$
4. $\text{the temperature of both must be the same}$

Solution:

$\text{Given: Solid and Hollow spheres with same material and radius}$ $\Delta Q = mc\Delta T$ $\Delta T = \frac{\Delta Q}{mc}$ $\text{For Hollow sphere, } \Delta T \text{ is more.}$ $\text{(as m is less for hollow sphere)}$ $\text{Now,}$ $\frac{\Delta V}{V} = \gamma \Delta T$ $\text{Therefore, the expansion in hollow is greater than the solid.}$

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
}