Import Question JSON

Current Question (ID: 19469)

Question:

$\text{An object of mass } m \text{ is placed at a height } R_e \text{ from the surface of the earth.}$ $\text{What is the increase in potential energy of the object if the height of the object is increased to } 2R_e \text{ from the surface?}$ $(R_e : \text{ Radius of the earth})$

Options:

1. $\frac{1}{3}mgR_e$
2. $\frac{1}{6}mgR_e$
3. $\frac{1}{2}mgR_e$
4. $\frac{1}{4}mgR_e$

Solution:

$U_i = -\frac{GM_em}{R_e + R_e}$ $U_f = -\frac{GM_em}{R_e + 2R_e}$ $\Delta U = U_f - U_i = \frac{GM_em}{6R_e} = \frac{mgR_e}{6}$

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
}