Import Question JSON

Current Question (ID: 19455)

Question:

$\text{Select the correct option based on the statements below:}$ $\text{Assertion (A): The escape velocities of planets } A \text{ and } B \text{ are the same. But } A \text{ and } B \text{ are of unequal mass.}$ $\text{Reason (R): The product of their mass and radius must be the same, } M_1R_1 = M_2R_2.$

Options:

1. $\text{Both (A) and (R) are True but (R) is not the correct explanation of (A).}$
2. $\text{(A) is True but (R) is False.}$
3. $\text{Both (A) and (R) are True and (R) is the correct explanation of (A).}$
4. $\text{(A) is False but (R) is True.}$

Solution:

$\text{Hint: } v_e = \sqrt{\frac{2GM}{R}}$ $\text{Explanation: The escape velocity is given by;}$ $v_{esc} = \sqrt{\frac{2GM}{R}}$ $\text{The conditions for equal escape speeds we get;}$ $v_1 = v_2$ $\sqrt{\frac{2GM_1}{R_1}} = \sqrt{\frac{2GM_2}{R_2}}$ $M_1R_2 = M_2R_1$ $\text{Therefore, Assertion (A) is correct.}$ $\text{As } M_1R_2 = M_2R_1$ $\text{The product of their mass and radius not be the same thus the Reason (R) is incorrect.}$ $\text{Hence, option (2) is the correct answer.}$

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
}