Import Question JSON

Current Question (ID: 19456)

Question:

$\text{The initial velocity } v_i \text{ required to project a body vertically upward from the surface of the earth to reach a height of } 10R, \text{ where } R \text{ is the radius of the earth, may be described in terms of escape velocity } v_e \text{ such that } v_i = \sqrt{\frac{x}{y}} \times v_e. \text{ The value of } x \text{ will be:}$ $1. \ 10$ $2. \ 20$ $3. \ 30$ $4. \ 40$

Options:

1. $10$
2. $20$
3. $30$
4. $40$

Solution:

$\text{Hint: Apply the conservation of energy.}$ $\frac{-GMm}{11R} = \frac{-GMm}{R} + \frac{1}{2}mv^2$ $v = \sqrt{\frac{20 \ GM}{11R}}$

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
}