Import Question JSON

Current Question (ID: 18958)

Question:

$\text{A beaker contains a fluid of density } p \text{ kg/m}^3, \text{ specific heat } S \text{ J/kg}^\circ\text{C and viscosity } \eta. \text{ The beaker is filled up to height } h. \text{ To estimate the rate of heat transfer per unit area } Q/A \text{ by convection when the beaker is put on a hot plate, a student proposes that it should depend on } \eta, \left( \frac{S \Delta \theta}{h} \right), \text{ and } \left( \frac{1}{pg} \right) \text{ when } \Delta \theta \text{ (in } ^\circ\text{C) is the difference in the temperature between the bottom and top of the fluid. In that situation, the correct option for } (Q/A) \text{ is:}$

Options:

1. $\eta \left( \frac{S \Delta \theta}{h} \right) \left( \frac{1}{pg} \right)$
2. $\eta \left( \frac{S \Delta \theta}{\eta h} \right) \left( \frac{1}{pg} \right)$
3. $\frac{S \Delta \theta}{\eta h} \left( \frac{1}{pg} \right)$
4. $\eta \frac{S \Delta \theta}{h}$

Solution:

$\text{Use the concept principle of homogeneity}$

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
}