Import Question JSON

Current Question (ID: 9718)

Question:

$\text{On the application of an impulsive force, a sphere of mass 500 grams starts moving with an acceleration of } 10 \text{ m/s}^2\text{. The force acts on it for } 0.5 \text{ s. The gain in the momentum of the sphere will be:}$

Options:

1. $2.5 \text{ kg-m/s}$
2. $5 \text{ kg-m/s}$
3. $0.05 \text{ kg-m/s}$
4. $25 \text{ kg-m/s}$

Solution:

$\text{Hint: Change in momentum = impulsive Force } \times \text{ time}$ $\text{Step 1:}$ $p_f - p_i = \frac{1}{2} \times 10 \times 0.5 \text{ (here, } p_i = 0\text{)}$ $p_f = 2.5 \text{ kg-m/s}$

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
}