Import Question JSON

Current Question (ID: 10218)

Question:

$\text{Given below are two statements:}$ $\text{Assertion (A): If the ice on the polar caps of the earth melts, then the length of the day will increase.}$ $\text{Reason (R): Moment of inertia of the earth increases, as ice on polar caps melts.}$

Options:

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

Solution:

$\text{When ice on the polar caps melts, the water redistributes from the poles (closer to Earth's axis of rotation) to the oceans (farther from the axis). This redistribution of mass increases Earth's moment of inertia.}$ $\text{According to the conservation of angular momentum, when the moment of inertia increases, the angular velocity must decrease to keep the angular momentum constant. Since the length of a day is inversely related to Earth's angular velocity, a decrease in angular velocity results in an increase in the length of the day.}$ $\text{Therefore, both statements are true: (A) the length of the day will increase, and (R) the moment of inertia increases. Moreover, (R) correctly explains why (A) occurs through the principle of conservation of angular momentum.}$ $\text{The final answer is option 1.}$

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
}