Import Question JSON

Current Question (ID: 19503)

Question:

$\text{A body of mass } m \text{ is projected with velocity } \lambda v_e \text{ in vertically upward}$ $\text{direction from the surface of the earth into space. It is given that } v_e \text{ is}$ $\text{escape velocity and } \lambda < 1. \text{ If air resistance is considered to be}$ $\text{negligible, then the maximum height from the centre of earth, to}$ $\text{which the body can go, will be: } (R: \text{ radius of earth})$

Options:

1. $\frac{R}{1+\lambda^2}$
2. $\frac{R}{1-\lambda^2}$
3. $\frac{R}{1-\lambda}$
4. $\frac{\lambda^2 R}{1-\lambda^2}$

Solution:

$\text{Hint: Conserve the mechanical energy of the system.}$

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
}