Import Question JSON

Current Question (ID: 19437)

Question:

$\text{The value of acceleration due to gravity at Earth's surface is } 9.8 \text{ ms}^{-2}. $ $\text{The altitude above its surface at which the acceleration due to gravity decreases to } 4.9 \text{ ms}^{-2}, \text{ is close to:}$ $\text{(Radius of earth = } 6.4 \times 10^6 \text{ m)}$

Options:

1. $6.4 \times 10^6 \text{ m}$
2. $9.0 \times 10^6 \text{ m}$
3. $2.6 \times 10^6 \text{ m}$
4. $1.6 \times 10^6 \text{ m}$

Solution:

$\text{Hint: } g_h = g_0 \left[ \frac{R_e}{R_e + h} \right]^2$ $\frac{GM}{(R + h)^2} = \frac{GM}{2R^2}$ $R + h = \sqrt{2}R$ $h = (\sqrt{2} - 1)R$ $\approx 2.6 \times 10^6 \text{ m}$

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
}