Import Question JSON

Current Question (ID: 9721)

Question:

$\text{A 100 kg gun fires a ball of 1 kg horizontally from a cliff at a height of 500 m. It falls on the ground at a distance of 400 m from the bottom of the cliff. The recoil velocity of the gun is: (Take } g = 10 \text{ m/s}^2\text{)}$

Options:

1. $0.2 \text{ m/s}$
2. $0.4 \text{ m/s}$
3. $0.6 \text{ m/s}$
4. $0.8 \text{ m/s}$

Solution:

$\text{Hint: As net force is zero so momentum will be conserved.}$ $\text{Step 1: The range of the ball is given by:}$ $R = u\sqrt{\frac{2H}{g}}$ $\Rightarrow u = 400 \times \sqrt{\frac{10}{2 \times 500}}$ $\Rightarrow u = 40 \text{ ms}^{-1}$ $\text{Step 2: Apply the conservation of momentum:}$ $0 = 40 \times 1 - 100 \times v$ $v = 0.4 \text{ ms}^{-1}$

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
}