Import Question JSON

Current Question (ID: 19207)

Question:

$\text{A bullet of mass } 10 \text{ g is fired from a gun (mass of } 10 \text{ kg without a bullet) with a speed of } 100 \text{ m/s. The recoil speed of the gun is:}$

Options:

1. $\frac{1}{10} \text{ m/s}$
2. $\frac{1}{5} \text{ m/s}$
3. $\frac{5}{2} \text{ m/s}$
4. $\frac{2}{5} \text{ m/s}$

Solution:

$\text{Hint: } p = mv$ $\text{Step: Find the recoil speed of the gun.}$ $\text{Given: } v_b = 100 \text{ m/s}, m_b = 10 \text{ g}, m_{gun} = 10 \text{ kg}$ $\text{The initial momentum of the bullet and gun is zero.}$ $\text{Applying the conservation of linear momentum, we get:}$ $0 = 10 \times v + 10 \times 10^{-3} \times 100$ $\Rightarrow 10 \times v = -1$ $\Rightarrow v = \frac{-1}{10} \text{ m/s}$ $\text{Therefore, the recoil speed of the gun is } \frac{1}{10} \text{ m/s.}$ $\text{Hence, option (1) is the correct answer.}$

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
}