Import Question JSON

Current Question (ID: 19657)

Question:

$\text{A lead bullet penetrates into a solid object and melts. Assuming that }$ $40\% \text{ of its kinetic energy is used to heat it, the initial speed of the bullet is: (Given, the initial temperature of the bullet = } 127^\circ\text{C,}$ $\text{Melting point of the bullet = } 327^\circ\text{C,}$ $\text{Latent heat of fusion of lead = } 2.5 \times 10^4 \text{ J Kg}^{-1}, \text{ Specific heat capacity of lead = } 125 \text{J/kg K)}$

Options:

1. $125 \text{ ms}^{-1}$
2. $500 \text{ ms}^{-1}$
3. $250 \text{ ms}^{-1}$
4. $600 \text{ ms}^{-1}$

Solution:

$\text{Let } m \text{ be the mass of the bullet.}$ $\text{Kinetic energy used for heating } = \frac{1}{2}mv^2 \times 0.4$ $= m \times 125 \times (327 - 127) + m \times 2.5 \times 10^4$ $\Rightarrow \frac{1}{2}v^2 \times 0.4 = 125 \times 200 + 2.5 \times 10^4$ $\Rightarrow v^2 = \frac{125 \times 200 + 2.5 \times 10^4}{0.2}$ $\Rightarrow v = 500 \text{ ms}^{-1}$

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
}