Import Question JSON

Current Question (ID: 19478)

Question:

$\text{Planet } A \text{ has a density and radius represented by } \rho \text{ and } R \text{ respectively, while planet } B \text{ has a density of } \frac{\rho}{2} \text{ and a radius of } 1.5R. \text{ If } g_{AS} \text{ and } g_{BS} \text{ denote the acceleration at the surface of planets } A \text{ and } B \text{ respectively, then the ratio } \frac{g_{BS}}{g_{AS}} =$

Options:

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

Solution:

$\text{Hint: } g = \frac{4\pi}{3} G \rho R$ $\text{Step: Find the ratio of acceleration due to gravity on the surface of the given planets.}$ $\therefore g = \frac{4\pi}{3} G \rho R$ $\therefore \frac{g_{BS}}{g_{AS}} = \frac{\rho_B R_B}{\rho_A R_A} = \left( \frac{\rho}{2} \right) (1.5R) \bigg/ \rho R = \frac{3}{4}$ $\text{Hence, option (2) is the correct answer.}$

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
}