Import Question JSON

Current Question (ID: 10737)

Question:

$\text{A piece of ice falls from a height } h \text{ so that it melts completely. Only one-quarter of the heat produced is absorbed by the ice, and all energy of ice gets converted into heat during its fall. The value of } h \text{ is:}$ $\text{(Latent heat of ice is } 3.4 \times 10^5 \text{ J/kg and } g = 10 \text{ N/kg)}$

Options:

1. $544 \text{ km}$
2. $136 \text{ km}$ (Correct)
3. $68 \text{ km}$
4. $34 \text{ km}$

Solution:

$\text{As per the conservation of energy, the energy gained by the ice during its fall from height h is given by:}$ $E = mgh$ $\text{As given, only one quarter of its energy is absorbed by the ice, so,}$ $\frac{mgh}{4} = mL_f$ $\Rightarrow h = \frac{mL_f \times 4}{mg}$ $= \frac{L_f \times 4}{g}$ $= 3.4 \times 10^5 \times \frac{4}{10} = 13.6 \times 10^4 = 13600 \text{m} = 136 \text{km}$

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
}