Import Question JSON

Current Question (ID: 19471)

Question:

$\text{A particle is released at a height equal to the radius of the earth above the surface of the earth. Its velocity when it hits the surface of the earth is equal to:}$ $\text{(Where, } M_e = \text{mass of earth, } R_e = \text{radius of the earth.)}$

Options:

1. $\sqrt{\frac{2GM_e}{R_e}}$
2. $\sqrt{\frac{GM_e}{2R_e}}$
3. $\sqrt{\frac{GM_e}{R_e}}$
4. $\sqrt{\frac{2GM_e}{3R_e}}$

Solution:

$\text{Applying law of conservation of mechanical energy,}$ $-\frac{GM_em}{2R_e} = -\frac{GM_em}{R_e} + \frac{1}{2}mv^2$ $v = \sqrt{\frac{GM_e}{R_e}}$

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
}