Import Question JSON

Current Question (ID: 19521)

Question:

$\text{Suppose a situation in which two planet orbits around the sun in the same orbit. If the mass of planet 1 is twice the mass of planet 2, then what do they have same?}$ $1. \text{Potential energy}$ $2. \text{Kinetic energy}$ $3. \text{Total energy}$ $4. \text{Velocity}$

Options:

1. $\text{Potential energy}$
2. $\text{Kinetic energy}$
3. $\text{Total energy}$
4. $\text{Velocity}$

Solution:

$\text{Hint: } v = \sqrt{\frac{GM}{r}} \text{ where } M = \text{mass of the sun.}$ $P.E. = -\frac{GMm}{r} \text{ m, different so different P.E.}$ $K.E. = \frac{1}{2}mv^2 \text{ m, different so different K.E.}$ $\text{T.E. will be different}$

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
}