Import Question JSON

Current Question (ID: 19652)

Question:

$\text{A bullet of mass } 5 \text{ g, travelling with a speed of } 210 \text{ m/s, strikes a fixed wooden target.}$ $\text{One half of its kinetic energy is converted into heat in the bullet while the other half is converted into heat in the wood.}$ $\text{The rise of temperature of the bullet if the specific heat of its material is } 0.03 \text{ cal/gm}^\circ\text{C (1 cal } = 4.2 \times 10^7 \text{ ergs) close to:}$

Options:

1. $83.3^\circ\text{C}$
2. $87.5^\circ\text{C}$
3. $119.2^\circ\text{C}$
4. $38.4^\circ\text{C}$

Solution:

$\text{Hint: } \frac{1}{2} \times \frac{1}{2} mv^2 = ms \Delta T$ $\frac{1}{2} mv^2 \times \frac{1}{2} = ms \Delta T$ $\Delta T = \frac{v^2}{4 \times 5} = \frac{210^2}{4 \times 30 \times 4.200}$ $= 87.5^\circ\text{C}$

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
}