Import Question JSON

Current Question (ID: 19654)

Question:

$\text{A 100 g of iron nail is hit by a 1.5 kg hammer striking at a velocity of 60 ms}^{-1}. \text{ What will be the rise in the temperature of the nail if one-fourth of the energy of the hammer goes into heating the nail?}$ $\text{[Specific heat capacity of iron = 0.42 Jg}^{-1} \cdot \text{°C}^{-1}]$

Options:

1. $675\text{°C}$
2. $1600\text{°C}$
3. $16.07\text{°C}$
4. $6.75\text{°C}$

Solution:

$\text{Hint: The heat energy} = \frac{1}{4} \times \text{The Kinetic energy}$ $\text{Step: Find the rise in the temperature of the nail.}$ $\text{Now, the rise in the temperature of the nail if one-fourth of the energy of the hammer goes into heating the nail is given by;}$ $\text{The heat energy} = \frac{1}{4} \times \text{The Kinetic energy}$ $mc\Delta T = \frac{1}{4} \times \frac{1}{2} mv^2$ $\frac{1}{8} \times 1.5 \times 3600 = 100 \times 0.42 \times \Delta T$ $1.5 \times 450 = 42(\Delta T)$ $\Delta T = \frac{1.5 \times 450}{42}$ $\Rightarrow \Delta T = 16.07\text{°C}$ $\text{Hence, option (3) is the correct answer.}$

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
}