Import Question JSON

Current Question (ID: 19459)

Question:

$\text{In the reported figure of earth, the value of acceleration due to gravity is same at point } A \text{ and } C \text{ but it is smaller than that of its value at point } B \text{ (surface of the earth). The value of } OA : OB \text{ will be:}$

Options:

1. $4 : 5$
2. $5 : 4$
3. $2 : 3$
4. $3 : 2$

Solution:

$\text{Hint: } E_g = \frac{GMr}{R^3}$ $g_A = \frac{GM(r)}{R^3}$ $g_C = \frac{GM}{\left(R + \frac{R}{2}\right)^2}$ $g_A = g_C$ $\frac{r}{R^3} = \frac{1}{4}R^2 \Rightarrow r = \frac{4R}{9}$ $\text{So, } OA = \frac{4R}{9} ; AB = R - r = \frac{5R}{9}$ $OA : AB = 4 : 5$

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
}